M. BASTI Bilal

MCA

Directory of teachers

Department

Mathematics Department

Research Interests

Fractional PDEs and Mathematical Physics Applications of Fractional Differential Equations Dynamical Systems and Their Applications Existence, Uniqueness, and Stability of Solutions Mathematical Biosciences and Numerical Simulations Dynamical Systems and Biomathematics Mathematical Modeling of Infectious and Insect Diseases

Contact Info

University of M'Sila, Algeria

Email : bilal.basti@univ-msila.dz

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Recent Publications

2025-10-10

On n-nonlinear Caputo fractional q-differential systems

This paper discusses the significance of quantum calculus in some mathematical fields. Itspecifically investigates solutions’ existence, uniqueness, and stability for a system of n-nonlinear fractionalq-differential equations with initial conditions involving Caputo fractional q-derivatives. The paper utilizesSchauder’s and Banach’s fixed-point theorems and Ulam-Hyers’ stability criteria to explore the analyticaldynamics inherent in these solutions. Additionally, it provides two illustrative examples to demonstratethe practical applicability of the obtained results.
Citation

M. BASTI Bilal, Salim Abdelkrim, , (2025-10-10), "On n-nonlinear Caputo fractional q-differential systems", [international] Filomat , Faculty of Sciences and Mathematics, University of Serbia

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2025-10-07

NONLINEAR FRACTIONAL Q-DIFFERENTIAL EQUATIONS INVOLVING HILFER-KATUGAMPOLA DERIVATIVES OFMOVING ORDERS

This study comprehensively investigates the existence, uniqueness, and stabilityof solutions for nonlinear fractional q-differential equations involving Hilfer-Katugampolaq-derivatives of moving orders. We apply the Banach contraction principle and Schauder’sfixed-point theorem to establish the existence of solutions. Furthermore, we examine thestability of the solutions using Ulam-Hyers theorems. Two detailed examples are providedto illustrate the practical applicability and validity of our theoretical results.
Citation

M. BASTI Bilal, (2025-10-07), "NONLINEAR FRACTIONAL Q-DIFFERENTIAL EQUATIONS INVOLVING HILFER-KATUGAMPOLA DERIVATIVES OFMOVING ORDERS", [international] Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis , Watam Press

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2024-12-15

Mathematical Insights to Control Epidemics Using Fractional Operators

In this paper, we discuss and provide some analytical studies for a mathematical model of fractional-order SIRD for COVID-19 in the sense of the Caputo-Katugampola derivative. We compute and derive several stability results based on some parameters that satisfy some conditions that prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SIRD model. It does so by applying the properties of Schauder's and Banach's fixed point theorems.
Citation

M. BASTI Bilal, (2024-12-15), "Mathematical Insights to Control Epidemics Using Fractional Operators", [international] International Conference on Mathematics and its Applications in Science and Technology , Setif 1 University Ferhat Abbas

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2024-12-07

Exploring nonlinear effects in fractional reaction-diffusion/wave equations

This paper studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.
Citation

M. BASTI Bilal, (2024-12-07), "Exploring nonlinear effects in fractional reaction-diffusion/wave equations", [national] 4th National Conference of Mathematics and Applications , Mila University Center

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2024-11-23

Traveling Profile Solutions for Parabolic Equations Describing Diffusion Phenomena

This paper aims to investigate and derive new exact solutions for a degenerate parabolic partial differential equation, specifically a nonlinear diffusion equation that is not in divergence form. We propose an approach inspired by the traveling profile method to obtain a general form of self-similar solutions to this equation. The behavior of these solutions depends on certain parameters, which determine whether their existence is global or local in a given time T.
Citation

M. BASTI Bilal, (2024-11-23), "Traveling Profile Solutions for Parabolic Equations Describing Diffusion Phenomena", [international] 17th African Conference on Research in Computer Science and Applied Mathematics-Digital Sciences in Africa , University of Bejaia, Algeria

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2024-11-06

Mathematical Exploration of Malaria Transmission Dynamics: Insights from Fractional Models and Numerical Simulation

This study presents an innovative mathematical model denoted as the fractional SIP(H)–SI(M) model, which aims to analyze and understand the dynamics of malaria transmission and spread. This model is distinguished by incorporating memory effects through fractional differential equations, allowing for a more accurate and realistic analysis of disease spread compared to traditional models. The proposed model is applied to Algeria by estimating its parameters using recent health data (from 2000). The results revealed that the disease‐free equilibrium is stable only when the basic reproduction number is less than one, indicating that controlling the spread of malaria and possibly eradicating it can be achieved by implementing appropriate preventive measures. Simulations also demonstrated a direct correlation between the rate of infection transmission and an increase in the number of infected individuals, highlighting the need for swift action when signs of an outbreak emerge. Based on these findings, a set of preventive measures is recommended, including insecticide spraying programs, widespread distribution of insecticide‐treated bed nets, and implementation of effective treatment protocols for infected individuals. This study also emphasizes the importance of continuous monitoring of health data and updating model parameters to ensure the effectiveness and sustainability of preventive measures.
Citation

M. BASTI Bilal, (2024-11-06), "Mathematical Exploration of Malaria Transmission Dynamics: Insights from Fractional Models and Numerical Simulation", [national] Advanced Theory and Simulations , Wiley-VCH GmbH

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2024-10-20

Analysis of fractional model for infectious diseases with a focus on chronic conditions in Algeria

This paper presents an in-depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters were estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (COVID-19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high-quality treatment, and precise isolation measures.
Citation

M. BASTI Bilal, (2024-10-20), "Analysis of fractional model for infectious diseases with a focus on chronic conditions in Algeria", [international] The Sixth International Colloquium on Methods and Tools for Decision Support , University Mouloud Mammeri of Tizi-Ouzou, Algeria

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2024-10-06

Modeling Physical Phenomena Using Fractional Partial Differential Equations

This paper studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.
Citation

M. BASTI Bilal, (2024-10-06), "Modeling Physical Phenomena Using Fractional Partial Differential Equations", [national] National Seminar on Modern Mathematics and Application , Mokhtar Badji University of Annaba, Algeria

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2024-09-12

Existence results for a coupled system of multi-term Katugampola fractional differential equations with integral conditions

This paper investigates a coupled system of nonlinear multi-term Katugampola fractional differential equations. Under sufficient conditions, it establishes the existence and uniqueness results of the solution by using standard fixed point theorems. Additionally, the paper includes some illustrative examples to strengthen the presented main results.
Citation

M. BASTI Bilal, (2024-09-12), "Existence results for a coupled system of multi-term Katugampola fractional differential equations with integral conditions", [national] Jordan Journal of Mathematics and Statistics , Deanship of Scientific Research, Yarmouk University, Irbid, Jordan.

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2024-08-23

Fractal model for predicting the spread of certain pandemics in society

In this paper, we discuss and provide some analytical studies for a mathematical model of fractional-order SIRD for COVID-19 in the sense of the Caputo-Katugampola derivative. We compute and derive several stability results based on some parameters that satisfy some conditions which prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SIRD model. It does so by applying the properties of Schauder's and Banach's fixed point theorems.
Citation

M. BASTI Bilal, (2024-08-23), "Fractal model for predicting the spread of certain pandemics in society", [international] The 24th International Pure Mathematics Conference 2024, Algebra, Analysis, and Geometry , University of Islamabad - Pakistan

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2024-06-01

Fractional Mathematical Model for Exploring the Influence of Infectious Diseases on Population with Chronic Conditions

This paper presents an in-depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters are estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (Tuberculosis and COVID-19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high-quality treatment, and precise isolation measures.
Citation

M. BASTI Bilal, (2024-06-01), "Fractional Mathematical Model for Exploring the Influence of Infectious Diseases on Population with Chronic Conditions", [national] Advanced Theory and Simulations , Wiley-VCH GmbH

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2023-12-13

Mathematical Modeling and Analysis for Studying the Behavior of Infectious Diseases

In our present work, we thoroughly examine and provide analytical insights into a mathematical models for infectious diseases as COVID-19, employing the Caputo-Katugampola derivative. Numerous stability results are meticulously computed based on well-defined parameters, ensuring compliance with conditions that effectively impede pandemic occurrences. Furthermore, the paper rigorously investigates the critical aspect of the existence and uniqueness of solutions for the SIRD model, leveraging the robust properties inherent in Schauder's and Banach's fixed point theorems. This multifaceted analysis not only enhances our understanding of the intricate dynamics of COVID-19 but also contributes valuable knowledge to the broader field of mathematical epidemiology.
Citation

M. BASTI Bilal, (2023-12-13), "Mathematical Modeling and Analysis for Studying the Behavior of Infectious Diseases", [national] Mathematical Modeling for Biology and Health "MMBS-2023" , Mohamed Boudiaf University of M'sila

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2023-11-26

Forecast and Analysis on the Spread of COVID-19 with Fractional Operators

In our present work, we thoroughly examine and provide analytical insights into a mathematical model characterizing the fractional-order SIRD dynamics for COVID-19, employing the Caputo-Katugampola derivative. Numerous stability results are meticulously computed based on well-defined parameters, ensuring compliance with conditions that effectively impede pandemic occurrences. Furthermore, the paper rigorously investigates the critical aspect of the existence and uniqueness of solutions for the SIRD model, leveraging the robust properties inherent in Schauder's and Banach's fixed point theorems. This multifaceted analysis not only enhances our understanding of the intricate dynamics of COVID-19 but also contributes valuable knowledge to the broader field of mathematical epidemiology.
Citation

M. BASTI Bilal, (2023-11-26), "Forecast and Analysis on the Spread of COVID-19 with Fractional Operators", [international] International Conference on Contemporary Mathematics and its Applications (ICCMA 2023) , Mila University Center, Algeria

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2023-11-20

Well-Posedness of the Multidimensional Nonlinear Free Energy Equation for Modeling Many Physical Phenomena

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.
Citation

M. BASTI Bilal, (2023-11-20), "Well-Posedness of the Multidimensional Nonlinear Free Energy Equation for Modeling Many Physical Phenomena", [international] Statistiques et Analyse Avancées: Domaines d'Interactions et d'Applications (SAADIA 1) , l’université de Bejaia, Algeria

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2023-10-18

Cauchy problem for Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics with fractional operators

In this paper, we examine the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems, while Caputo’s fractional derivative is used as the differential operator. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.
Citation

M. BASTI Bilal, (2023-10-18), "Cauchy problem for Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics with fractional operators", [national] Annals of the Alexandru Ioan Cuza University - Mathematics , Universitatii Al.I.Cuza din Iasi

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2023-09-01

Theoretical Studies on the Existence and Uniqueness of Solutions for a Multidimensional Nonlinear Time and Space-Fractional Reaction-Diffusion/Wave Equation

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, application of Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation. The applicability of our main results is demonstrated through examples and explicit solutions.
Citation

M. BASTI Bilal, (2023-09-01), "Theoretical Studies on the Existence and Uniqueness of Solutions for a Multidimensional Nonlinear Time and Space-Fractional Reaction-Diffusion/Wave Equation", [national] Memoirs on Differential Equations and Mathematical Physics , Andrea Razmadze Mathematical Institute

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2023-08-26

A hybrid model for a class of multidimensional nonlinear free energy equations

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.
Citation

M. BASTI Bilal, (2023-08-26), "A hybrid model for a class of multidimensional nonlinear free energy equations", [international] 23rd International Pure Mathematics Conference , University of Islamabad - Pakistan

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2023-07-04

View analysis of nonlinear acoustic wave equations in terms of viscoelasticity

This paper examines the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Banach's fixed point theorem.
Citation

M. BASTI Bilal, (2023-07-04), "View analysis of nonlinear acoustic wave equations in terms of viscoelasticity", [national] The Second Online National Conference on Pure and Applied Mathematics , Université Echahid Cheikh Larbi Tebessi– Tebessa, Algeria

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2023-06-28

ANALYTICAL STUDIES FOR A HYBRID MATHEMATICAL MODEL OF COVID-19: THE INFLUENCE OF THE PANDEMIC ON CHRONICALLY ILL PEOPLE

This paper discusses and provides some analytical studies for a hybrid mathematical model of COVID-19, which is a SECIRD fractional model that is concerned with the influence of the pandemic on chronically ill people. We compute and derive several stability results based on some parameters that satisfy some conditions that prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SECIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.
Citation

M. BASTI Bilal, (2023-06-28), "ANALYTICAL STUDIES FOR A HYBRID MATHEMATICAL MODEL OF COVID-19: THE INFLUENCE OF THE PANDEMIC ON CHRONICALLY ILL PEOPLE", [international] 2nd Edition of the International Symposium & International Student Workshop on Interdisciplinary Mathematics in the CiTi areas (ISIM & ISWIM) , National University of Science and Technology POLITEHNICA Bucharest, Romania

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2023-06-01

Thermodynamical Problem of High-Frequency Ultra Sound Waves Equation with Fractional Operators

Nonlinear fractional partial differential equations (PDEs) have been used to model many phenomena in various fields, such as mathematics and physics, and the evolution of phenomena in different scientific areas. The property of the fractional derivative operators plays an especially crucial role in applied mathematics and physics. Exact solutions of fractional equations are used to mathematically formulate and, thus, aid in defining the solution of physical and other problems, including functions of several variables such as the propagation of heat or sound, etc. Several mathematical models are used to describe nonlinear acoustic phenomena. For example, in this work, we shall give a fractional model of nonlinear acoustics named the space-fractional Jordan-Moore-Gibson-Thompson (JMGT) equation. This equation results from modeling high-frequency ultrasound waves.
Citation

M. BASTI Bilal, (2023-06-01), "Thermodynamical Problem of High-Frequency Ultra Sound Waves Equation with Fractional Operators", [international] International Conference of Young Mathematicians , The Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine

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2023-05-14

Effective results concerning new functional solutions of fractional hyperbolic problems with an inverse source term

This paper investigates the problem of the existence and uniqueness of one solution under the traveling wave form for a free boundary problem of a space-fractional wave equation with an inverse source term. It does so by applying Banach's fixed point theorem.
Citation

M. BASTI Bilal, (2023-05-14), "Effective results concerning new functional solutions of fractional hyperbolic problems with an inverse source term", [national] The first National Applied Mathematics Seminar , Mohamed Khider University of Biskra, Algeria

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2023-05-13

Application of Fractional Calculus in The Modeling of Biological Phenomena and Infectious Diseases

In this paper, we discuss and provide some analytical studies for a mathematical model of fractional-order SEIRD for COVID-19 in the sense of the Caputo-Katugamp ola derivative. We compute and derive several stability results based on some parameters that satisfy some conditions that prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SEIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed-point theorem.
Citation

M. BASTI Bilal, (2023-05-13), "Application of Fractional Calculus in The Modeling of Biological Phenomena and Infectious Diseases", [national] Second National Conference on Applied Mathematics and Didactics , Ecole Normale Supérieure Assia Djebar – Constantine, Algeria

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2023-01-10

Existence Study of Solutions for a System of n-Nonlinear Fractional Differential Equations with Integral Conditions

This paper offers a thorough discussion and study of the existence and uniqueness of solutions proposed for a class of new systems of n-nonlinear fractional differential equations and their main properties using the fractional derivative of Katugampola with n integral conditions. Schauder’s fixed point theorem, the Banach contraction principle, and Leray-Schauder type nonlinear alternative are applied to attain the desired goal. In order to exhibit the usefulness of our main results, several examples are also presented in the paper.
Citation

M. BASTI Bilal, (2023-01-10), "Existence Study of Solutions for a System of n-Nonlinear Fractional Differential Equations with Integral Conditions", [national] Journal of Mathematical Physics, Analysis, Geometry , ILTPE-B. Verkin Institute for Low Temperature Physics and Engineering

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2022-12-18

Thermo-viscous elastic free boundary problem of fractional PDEs of nonlinear acoustics

This paper examines the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Banach's fixed point theorem.
Citation

M. BASTI Bilal, (2022-12-18), "Thermo-viscous elastic free boundary problem of fractional PDEs of nonlinear acoustics", [national] THE SECOND NATIONAL CONFERENCE ON PURE AND APPLIED MATHEMATICS (NCPAM2022) , Amar Telidji University of Laghouat, Algeria

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2022-09-27

Existence Of Traveling Wave Solutions For A Free Boundary Problem Of Higher-Order Space-Fractional Wave Equations

The fractional wave equation of higher order is presented as a generalization of the higher-order wave equation when arbitrary fractional-order derivatives are involved. This paper investigates the problem of existence and uniqueness of solutions under the traveling wave forms for a free boundary problem of higher-order space-fractional wave equations. It does so by applying the properties of Schauder's and Banach's fixed point theorems.
Citation

M. BASTI Bilal, (2022-09-27), "Existence Of Traveling Wave Solutions For A Free Boundary Problem Of Higher-Order Space-Fractional Wave Equations", [national] Applied Mathematics E - Notes , Tsinghua University

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2022-03-10

Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order

This paper particularly addresses and discusses some analytical studies on the existence and uniqueness of global or blow-up solutions under the traveling profile forms for a free boundary problem of two-dimensional diffusion equations of moving fractional order. It does so by applying the properties of Schauder's and Banach's fixed-point theorems. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.
Citation

M. BASTI Bilal, (2022-03-10), "Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order", [national] Advances in the Theory of Nonlinear Analysis and its Application , DergiPark

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2021-08-04

Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.
Citation

M. BASTI Bilal, (2021-08-04), "Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives", [national] Symmetry , Multidisciplinary Digital Publishing Institute (MDPI)

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2021-05-29

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.
Citation

M. BASTI Bilal, (2021-05-29), "Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions", [national] Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica , Sciendo, De Gruyter Brill company

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2020-09-05

Global Existence And Blow-Up Of Generalized Self-Similar Solutions To Nonlinear Degenerate Diffusion Equation Not In Divergence Form

This paper investigates the problem of existence and uniqueness of positive solutions under the general self-similar form of the degenerate parabolic partial differential equation which is known as "nonlinear diffusion equation not in divergence form". By applying the properties of Banach's fixed point theorems, we establish several results on the existence and uniqueness of the general form of self-similar solutions of this equation.
Citation

M. BASTI Bilal, (2020-09-05), "Global Existence And Blow-Up Of Generalized Self-Similar Solutions To Nonlinear Degenerate Diffusion Equation Not In Divergence Form", [national] Applied Mathematics E - Notes , Tsinghua University

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2020-04-16

Existence results for nonlinear Katugampola fractional differential equations with an integral condition

This work studies the existence and uniqueness of solutions for a class of nonlinear fractional differential equations via the Katugampola fractional derivatives with an integral condition. The arguments for the study are based up on the Banach contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type.
Citation

M. BASTI Bilal, (2020-04-16), "Existence results for nonlinear Katugampola fractional differential equations with an integral condition", [national] Acta Mathematica Universitatis Comenianae , Univerzita Komenskeho

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2020-02-07

Existence Results of Self-similar Solutions to The Caputo-type’s Space-fractional Heat Equation

This paper investigates the problem of existence and uniqueness of solutions under the self-similar forms to the space-fractional heat equation. By applying the properties of Banach's fixed point theorems, Schauder's fixed point theorem and the nonlinear alternative of Leray-Schauder type, we establish several results on the existence and uniqueness of self-similar solutions to this equation.
Citation

M. BASTI Bilal, (2020-02-07), "Existence Results of Self-similar Solutions to The Caputo-type’s Space-fractional Heat Equation", [national] Surveys in Mathematics and its Applications , University Constantin Brancusi of Targu-Jiu

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2019-07-31

Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For application purposes, some examples are provided to demonstrate the usefulness of our main results.
Citation

M. BASTI Bilal, (2019-07-31), "Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations", [national] Journal of Mathematics and Applications , Rzeszów University of Technology.

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2019-05-04

Existence et unicité de solutions auto-similaires générales pour certaines équations fractionnaires non-linéaires

In this thesis, we discuss several existence and uniqueness results of generalized self-similar solutions for some nonlinear partial differential equations of fractional order of Katugampola type, with boundary value, initial value, or with integral conditions in Banach space, we use the Banach contraction principle, Schauder and Guo-Krasnosel'skii fixed point theorems, and the technique of the nonlinear alternative of Leray-Schauder type.
Citation

M. BASTI Bilal, (2019-05-04), "Existence et unicité de solutions auto-similaires générales pour certaines équations fractionnaires non-linéaires", [national] Mohamed Boudiaf University of M'sila

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2019-01-01

Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola Derivative

This work studies the existence and uniqueness of solutions for a class of nonlinear implicit fractional differential equations via the Katugampola fractional derivatives with an initial condition. The arguments for the study are based upon the Banach contraction principle, Schauder's fixed point theorem, and the nonlinear alternative of Leray-Schauder type.
Citation

M. BASTI Bilal, (2019-01-01), "Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola Derivative", [national] Applied Mathematics E - Notes , Tsinghua University

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