M. ARIOUA Yacine

Prof

Directory of teachers

Department

Mathematics Department

Research Interests

Fractional differential equations, Partial differential equations and Fractional calculus,

Contact Info

University of M'Sila, Algeria

Email : yacine.arioua@univ-msila.dz

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Recent Publications

2025-11-25

THE FUNDAMENTAL AND GLOBAL EXISTENCE OF SOLUTIONSTO A GENERALIZED NONLINEAR FRACTIONAL DIFFUSIONEQUATION WITH GRADIENT NONLINEARITY

This paper studies the existence of global solutions to a nonlinear fractional diffusion equation involving a ψ-Caputo derivative. A fundamental solution to the linear case is derived by employing the ψ-Laplace transformand Fox H-functions. A decay estimate for the solution in Lebesgue spaces is then established. Finally, theexistence, uniqueness, and well-posedness of mild global solutions to the nonlinear fractional diffusion equationare demonstrated under small initial data and modified norms.
Citation

M. ARIOUA Yacine, (2025-11-25), "THE FUNDAMENTAL AND GLOBAL EXISTENCE OF SOLUTIONSTO A GENERALIZED NONLINEAR FRACTIONAL DIFFUSIONEQUATION WITH GRADIENT NONLINEARITY", [international] Journal of Mathematical Sciences , Springer Nature Switzerland

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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. ARIOUA Yacine, 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. ARIOUA Yacine, (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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2025-03-18

Homotopy Perturbation ρ-Laplace Transform Approach for Numerical Simulation of Fractional Navier-Stokes Equations

In this study, we tackle the time fractional discrete Navier-Stokes equation by employing the homotopyperturbation ρ-Laplace transform method (HPLTM), utilizing the Caputo-Katugampola fractional derivative of time.Additionally, we present graphical representations of the solution generated using Matlab software, comparing it withthe exact solution for α = 1. We perform two test problems to verify and demonstrate the effectiveness of our approach.Our numerical findings and graphical analyses indicate that the proposed approach exhibits remarkable efficiency andsimplicity, rendering it suitable for addressing a diverse array of challenges encountered in engineering and the sciences
Citation

M. ARIOUA Yacine, Awatif Alghahtani, , (2025-03-18), "Homotopy Perturbation ρ-Laplace Transform Approach for Numerical Simulation of Fractional Navier-Stokes Equations", [international] Contemporary Mathematics , Universal Wiser Publisher

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2024-12-31

Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method

The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace transform (LT). The time-fractional derivative used is the Caputo–Hadamard fractional derivative (CHFD). The effectiveness of this method is demonstrated and validated through two test problems. The results show that the proposed method is robust, efficient, and easy to implement for both linear and nonlinear problems in science and engineering. Additionally, its computational efficiency requires less computation compared to other schemes
Citation

M. ARIOUA Yacine, mihobi.hamza@univ-msila.dz, Alqahtani, A.M, Bouderah, B, , (2024-12-31), "Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method", [national] Fractal Fract , MDPI

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2024-12-07

LOCAL EXISTENCE FOR AN INTEGRO-DIFFERENTIAL DIFFUSION EQUATION WITH NONLOCAL NONLINEARITIES

LOCAL EXISTENCE FOR AN INTEGRO-DIFFERENTIAL DIFFUSION EQUATION WITH NONLOCAL NONLINEARITIES
Citation

M. ARIOUA Yacine, (2024-12-07), "LOCAL EXISTENCE FOR AN INTEGRO-DIFFERENTIAL DIFFUSION EQUATION WITH NONLOCAL NONLINEARITIES", [national] 4th National Conference of Mathematics and Applications (CNMA – 2024) , University Center of Mila, Algeria

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2024-09-02

The Local Existence of Solution to Caputo Katugampola Fractional Integro-differential Equation

The Local Existence of Solution to Caputo Katugampola Fractional Integro-differential Equation
Citation

M. ARIOUA Yacine, (2024-09-02), "The Local Existence of Solution to Caputo Katugampola Fractional Integro-differential Equation", [international] 3rd international symposium on current developments in fondamental and applied mathematics sciences , Turkey

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2024-05-14

The Blow-Up Existence of Solution to Caputo–Katugampola Fractional Partial Differential Equation with Fractional Laplace

1st International Conference on Nonlinear Mathematical Analysis and its Applications
Citation

M. ARIOUA Yacine, (2024-05-14), "The Blow-Up Existence of Solution to Caputo–Katugampola Fractional Partial Differential Equation with Fractional Laplace", [national] 1st International Conference on Nonlinear Mathematical Analysis and its Applications (IC-NMAA'24) , Bordj Bou Arréridj University

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2023-12-21

Existence of Traveling Profiles Solutions to Porous Medium Equation

In this paper, we shall study the existence and uniqueness of solutions called "traveling profiles solutions" to the porous medium equation in one dimension. By these solutions, we generalize the results obtained by Gilding and Peletier who proved the existence of self similar solutions of type I, II and III to the same equation. The principal idea of our work is to convert the porous media equation in to an equivalent
nonlinear differential equation, and to prove the existence and uniqueness of these new solutions under certain conditions.
Citation

M. ARIOUA Yacine, (2023-12-21), "Existence of Traveling Profiles Solutions to Porous Medium Equation", [national] Journal officiel Mathematics and Application , Publishing House of Rzeszów University of Technology P.O. Box 85, 35-959 Rzeszów, Poland

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2023-05-16

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. ARIOUA Yacine, Basti Bilal, , (2023-05-16), "Existence Study of Solutions for a System of n Nonlinear Fractional Differential Equations with Integral Conditions", [national] Journal of Mathematical Physics, Analysis, Geometry , National Academy of Sciences of Ukraine B.Verkin Institute for Low Temperature Physics and Engineering.

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2023-04-03

Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative

In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional
diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity vari-
able η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed
point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).
Citation

M. ARIOUA Yacine, Ouagueni Nora, , (2023-04-03), "Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative", [national] Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica , Sciendo

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2023-03-13

Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative

This paper is devoted to the existence and uniqueness of solution to a class of Hadamard fractional differential equation under fractional Sobolev spaces. A novel form of fractional Sobolev space via Hadamard fractional operator is well proposed and related properties are also proved. Furthermore, a variational formulation of considered system is established and thereby the Lax-Milgram theorem is also employed to demonstrate the existence and uniqueness.
Citation

M. ARIOUA Yacine, (2023-03-13), "Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative", [national] Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES , Bulletin, Institute of Mathematics, Academia Sinica

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2023

Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative

In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard derivative. To do so, we have used a
finite difference method. The Convergence and stability of the given finite difference scheme are studied using the mathematical induction technique. Moreover, Numerical examples are
given to demonstrate the effectiveness of our results.
Citation

M. ARIOUA Yacine, (2023), "Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative", [national] International Journal of Applied and Computational Mathematics , Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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2022

The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative

In this paper, a numerical approximation solution of a space-time fractional diffusion equation (FDE), involving Caputo-Katugampola fractional derivative is considered. Stability and convergence of the proposed scheme are discussed using mathematical induction. Finally, the proposed method is validated through numerical simulation results of different examples.
Citation

M. ARIOUA Yacine, (2022), "The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative", [national] Numerical Algebra, Control and Optimization , Bulent Karasozen

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Numerical solutions for linear fractional differential equation with dependence on the Caputo-Hadamard derivative using finite difference method

The main objective of this paper is to find accurate solutions for linear fractional differential equations involving the fractional Caputo-Hadamard derivative of order α > 0. Therefore, to achieve this objective, a new method called the Finite Fractional Difference Method (FFDM) is employed to find the numerical solution. As such, the convergence and stability of
the numerical scheme is discussed and illustrated by solving two linear fractional differential equation problems of order 0 < α<=1 to show the validity of our method.
Citation

M. ARIOUA Yacine, (2022), "Numerical solutions for linear fractional differential equation with dependence on the Caputo-Hadamard derivative using finite difference method", [national] Palestine Journal of Mathematics , Nouressadat Touafek

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Existence and uniqueness results of self-similar solutions of the space-fractional diffusion equation

Existence and uniqueness results of self-similar solutions of the space-fractional diffusion equation
Citation

M. ARIOUA Yacine, Nora ouagueni, , (2022), "Existence and uniqueness results of self-similar solutions of the space-fractional diffusion equation", [international] 3rd International Conference on Applied Engineering and Natural Sciences , Konya/Turkey

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Existence And Uniqueness Of Solution For A Mixed-Type Fractional Di¤erential Equation And Ulam-Hyers Stability

In this paper, we have discussed a special type of nonlinear boundary value problems (BVPs) which involves both the right-sided Caputo-Katugampola (CK) and the left-sided Katugampola fractional derivatives (FDs). Based on some new techniques and some properties of the Mittag-Le er functions, we have introduced a formula of the solution for the aforementioned problem. To study the existence and uniqueness results of the solution for this problem, we have applied some known xed point theorems (i.e., Banachs contraction principle, Schauders xed point theorem, nonlinear alternative of Leray-Schauder type and Schaefers xed point theorem). We have also studied the Ulam-Hyers stability of this problem. To illustrate the theoretical results in this work, we have given two examples.
Citation

M. ARIOUA Yacine, Nora Ouagueni, , (2022), "Existence And Uniqueness Of Solution For A Mixed-Type Fractional Di¤erential Equation And Ulam-Hyers Stability", [national] Applied Mathematics E-not , Tsing Hua University Hsinchu, TAIWAN

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2021

ON CRITERIA OF EXISTENCE FOR NONLINEAR KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS WITH p–LAPLACIAN OPERATOR

This paper is devoted to establishing vital criteria of existence and uniqueness for a class of nonlinear Katugampola fractional differential equations (KFDEs) with p-Laplacian operator subjecting to mixed boundary conditions. The reasoning is inspired by diverse classical f ixed point theory, such as the Guo-Krasnosel’skii type fixed point principle and Banach contraction theorem. Additionally, several expressive examples are afforded to show the effectiveness of our theoretical results.
Citation

M. ARIOUA Yacine, Li Ma, , (2021), "ON CRITERIA OF EXISTENCE FOR NONLINEAR KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS WITH p–LAPLACIAN OPERATOR", [national] Fractional Differential Calculus , www.ele-math.com

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Boundary value problem for nonlinear fractional differential equations involving Erd´elyi–Kober derivative on unbounded domain

In this paper, we establish sufficient conditions for the existence of bounded solution for a class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi–Kober differential operator on unbounded domain. Our results are based on a fixed point theorem of Schauder combined with the diagonalization argument method in a special Banach space. To that end, an example is presented to illustrate the usefulness of our main results.
Citation

M. ARIOUA Yacine, Maria Titraoui, , (2021), "Boundary value problem for nonlinear fractional differential equations involving Erd´elyi–Kober derivative on unbounded domain", [national] Annals of the University of Craiova, Mathematics and Computer Science Series , University of Craiova

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Boundary Value Problem For A Coupled System Of Nonlinear Fractional Differential Equations Involving Erdélyi-Kober Derivative

In this paper, we focus on the boundary value problem (BVP) for a coupled system of nonlinear fractional differential equations (SFDEs) involving the Erdélyi-Kober derivatives on an innite interval. First, we dene the integral solution of the BVP for Erdélyi-Kober (SFDEs). Then, by using the Banach contraction principle and the Leray-Schauder nonlinear alternative xed point theorem in a special Banach space, existence and uniqueness theorems of the given problem are demonstrated, respectively. Finally, several indispensable examples are presented to illustrate the usefulness of our main results.
Citation

M. ARIOUA Yacine, Maria Titraoui, , (2021), "Boundary Value Problem For A Coupled System Of Nonlinear Fractional Differential Equations Involving Erdélyi-Kober Derivative", [national] Applied mathematics E-Notes , China

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2020

UNBOUNDED SOLUTION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-TYPE ERDELYI KOBER FRACTIONAL DIFFERENTIAL EQUATION ON THE HALF-LINE

In this paper, we investigate the existence and uniqueness of solutions to a class of boundary value problem of nonlinear Caputo type Erdély Kober fractional differential equations
Citation

M. ARIOUA Yacine, (2020), "UNBOUNDED SOLUTION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-TYPE ERDELYI KOBER FRACTIONAL DIFFERENTIAL EQUATION ON THE HALF-LINE", [international] Dynamic of Continuous Discrete and Impulsive Systems Serie A , Watam Press , Canada

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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. ARIOUA Yacine, Basti Bilal, , (2020), "Existence results for nonlinear Katugampola fractional differential equations with an integral condition", [national] Acta Mathematica Universitatis Comenianae , Comenius University, 842 48 Bratislava, Slovak Republic

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2019-11-21

Fractional Differential Equations of Caputo- Katugampola Type and numerical Solutions

The objective of this present work is to study various approaches to the numerical solution of fractional partial differential equations (FPDEs) of the Caputo-Katugampola type. Among the intriguing methods explored in our study, we emphasize the Adomian Decomposition Method (ADM), the Homotopy Perturbation Method (HPM), and the Iterative Decomposition Method (IDM).
Citation

M. ARIOUA Yacine, (2019-11-21), "Fractional Differential Equations of Caputo- Katugampola Type and numerical Solutions", [international] RAMA 11 , Sidi Bel Abbès

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2019

New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative

In this paper, we introduce a new class of boundary value
problem for nonlinear fractional di erential equations involving the Erdélyi-
-Kober differential operator on an in nite interval. Existence and uniqueness
results for a positive solution of the given problem are obtained by
using the Banach contraction principle, the Leray-Schauder nonlinear alternative,
and Guo-Krasnosel'skii xed point theorem in a special Banach
space. To that end, some examples are presented to illustrate the usefulness
of our main results
Citation

M. ARIOUA Yacine, Titraoui Maria, , (2019), "New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative", [national] Communications in Mathematics , University of Ostrava, Czech Republic

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Initial Value Problem for a Coupled System of Katugampola-Type Fractional Differential Equations

The aim of this work is to study the initial value problem of a coupled system of
nonlinear fractional differential equations with Katugampola derivative. Some new
existence and uniqueness results of solutions for the given problems are obtained
by using the Banach contraction principle, Schauder’s and nonlinear alternative
Leray–Schauder fixed point theorems. Several examples are presented to illustrate
the usefulness of our main results
Citation

M. ARIOUA Yacine, (2019), "Initial Value Problem for a Coupled System of Katugampola-Type Fractional Differential Equations", [national] Advances in Dynamical Systems and Applications , Research India Publications

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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 xed point theo-
rems. For applications purposes, some examples are provided to demon-
strate the usefulness of our main results.
Citation

M. ARIOUA Yacine, Basti Bilal, , (2019), "Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations", [national] Journal of Mathematics and Applications , Publishing House of Rzeszow University of Technology, Poland

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Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola

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, Schauders fixed point theorem and the nonlinear
alternative of Leray-Schauder type
Citation

M. ARIOUA Yacine, Basti bilal, , (2019), "Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola", [national] Applied Mathematics E-Notes , Tsing Hua University Hsinchu, TAIWAN

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2017

Boundary value problem for Caputo-Katugampola fractional differential equations

Boundary value problem for Caputo-Katugampola fractional differential equations
Citation

M. ARIOUA Yacine, (2017), "Boundary value problem for Caputo-Katugampola fractional differential equations", [national] Journeés doctoral JDO2017 , Université de M'sila

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Existence results for nonlinear fractional differential equations with Caputo-Hadamard derivative

Existence results for nonlinear fractional differential equations with Caputo-Hadamard derivative
Citation

M. ARIOUA Yacine, (2017), "Existence results for nonlinear fractional differential equations with Caputo-Hadamard derivative", [national] Mathématiques en images, MI’2017 , Université de M'sila

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BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS

The aim of this work is to study the existence and uniqueness solutions for boundary
value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in
bounded domain. We used the standard and Krasnoselskii’s fixed point theorems. Some new results
of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained
Citation

M. ARIOUA Yacine, (2017), "BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS", [international] Surveys in Mathematics and its Applications , Bucharest University, Romania

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2016

Traveling profiles solutions to heat equation with a power-law nonlinearity

Traveling profiles solutions to heat equation with a power-law nonlinearity
Citation

M. ARIOUA Yacine, (2016), "Traveling profiles solutions to heat equation with a power-law nonlinearity", [national] Congrès des Mathématiciens Algériens CMA'2016 , Université de Batna

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Existence of general self similar solution to porous medium equation

In this paper, we propose a general self similar solutions to the porous medium.
We also discuss their existence for some initial data in one dimension. We find
for some particular cases an explicit exact solutions. these
solutions are called "travelling pro…le solutions".
Citation

M. ARIOUA Yacine, (2016), "Existence of general self similar solution to porous medium equation", [international] International Arab Conference on Mathematics and Computations (2016), , Zarqa University, Jordan

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2012

Solutions de l'équation des milieux poreux par la méthode des profiles mobiles

Solutions de l'équation des milieux poreux par la méthode des profiles mobiles
Citation

M. ARIOUA Yacine, (2012), "Solutions de l'équation des milieux poreux par la méthode des profiles mobiles", [national] Congrès des Mathématiciens Algériens CMA'2012 , Université de Annaba

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2009

New Method for Constructing Exact Solutions to Nonlinear PDEs

We propose in this paper a new approach to construct exact solutions of nonlinear
PDEs. The method used is called ”the travelling profiles method”. The travelling profiles
method enables us to obtain many exact solutions to large classes of nonlinear PDEs
Citation

M. ARIOUA Yacine, (2009), "New Method for Constructing Exact Solutions to Nonlinear PDEs", [national] International Journal of Nonlinear Science , World Academic Press, World Academic Union, England, UK

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2007

New exact solutions to porous medium equation with traveling wavelets in one dimension

New exact solutions to porous medium equation with traveling wavelets in one dimension
Citation

M. ARIOUA Yacine, (2007), "New exact solutions to porous medium equation with traveling wavelets in one dimension", [international] 2ièm colloque internationale sur l'analyse non linéaire et applications (ANL'07) , Université de Sétif

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2006

Etude de l'équation de Fujita par la méthode des Ondelettes mobiles

Etude de l'équation de Fujita par la méthode des Ondelettes mobiles
Citation

M. ARIOUA Yacine, (2006), "Etude de l'équation de Fujita par la méthode des Ondelettes mobiles", [international] Rencontre internationale d'analyse mathématique et ses applications (RAMA V) , Université de M'sila

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2005

Participation in the CIMPA-UNSA-UNESCO school

Financial markets modeling
Citation

M. ARIOUA Yacine, (2005), "Participation in the CIMPA-UNSA-UNESCO school", [international] Financial markets modeling , University of Irbid, Jordan

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