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Mathematics Department
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Recent Publications
ON THE EXISTENCE AND UNIQUENESS OF TH WEAK SOLUTION TO SPATIAL FRACTIONAL NONLINEAR DIFFUSION EQUATION RELATED TO IMAGE PROCESSING
diffusion equation, which can be applied in image processing. The proposed model combines the
advantages of both second- and fourth-order diffusion equations along with Gaussian filtering
by employing spatial fractional derivatives and a Gaussian filter. This approach enhance edges
preservation and robustness to noise. The existence and uniqueness of the weak solution for the
model are proved by applying Schauder’s fixed-point theorem.
Citation
M. BENHAMIDOUCHE Noureddine, (2025-02-28), "ON THE EXISTENCE AND UNIQUENESS OF TH WEAK SOLUTION TO SPATIAL FRACTIONAL NONLINEAR DIFFUSION EQUATION RELATED TO IMAGE PROCESSING", [national] MATHEMATICA SCANDINAVICA , Institut for Matematik Aarhus Universitet
Mathematical Exploration of Malaria Transmission Dynamics: Insights from Fractional Models and Numerical Simulation
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. BENHAMIDOUCHE Noureddine, (2025-02-02), "Mathematical Exploration of Malaria Transmission Dynamics: Insights from Fractional Models and Numerical Simulation", [national] Advanced Theory and Simulations , © Wiley-VCH GmbH, Weinheim
ADDITIVE OPERATOR SPLITTING SCHEME FOR A GENERAL MEAN CURVATURE FLOW AND APPLICATION IN EDGES ENHANCEMENT
have been extensively applied for different tasks in image processing. Among
these PDE-based approaches, the mean curvature flow filtering has impressive
results, for which feature directions in the image are important.
In this paper, we explore a general model of mean curvature flow, as proposed
in [G.I. Barenblatt, Self-similar intermediate asymptotics for nonlinear
degenerate parabolic free-boundary problems that occur in image processing, Proceedings
of the National Academy of Sciences of the United States of America
(2001)], [ G.I. Barenblatt and J.L. Vazquez, Nonlinear diffusion and image
contour enhancement, Interfaces and Free Boundaries (2003)]. The model can be
re-arranged to a reaction-diffusion form, facilitating the creation of an unconditionally
stable semi-implicit scheme for image filtering. The method employs the
Additive Operator Split (AOS) technique. Experiments demonstrated that the
modified general model of mean curvature flow is highly effective for reducing
noise and has a superior job of preserving edges.
Citation
M. BENHAMIDOUCHE Noureddine, (2024-12-14), "ADDITIVE OPERATOR SPLITTING SCHEME FOR A GENERAL MEAN CURVATURE FLOW AND APPLICATION IN EDGES ENHANCEMENT", [national] JOURNAL OF NUMERICAL ANALYSIS AND APPROXIMATION THEORY , Tiberiu Popoviciu Institute of Numerical Analysis
SELF-SIMILAR SOLUTIONS FOR A NEW FREE-BOUNDARY PROBLEM AND IMAGE CONTOUR ENHANCEMENT
ment in image processing, based on a new evolution model consider as a generalization
of mean curvature motion. A free boundary problem is formulated describing the image
intensity evolution in the boundary layers around the edges of image. An asymptotic self-
similar solutions to this nonlinear di usion equation are obtained in explicit forms. The
solutions demonstrated that the edge enhancement and its rates depends on the parame-
ters of equation. The experimental results demonstrate the e ectiveness of the model in
edge preservation.
Citation
M. BENHAMIDOUCHE Noureddine, (2024-10-10), "SELF-SIMILAR SOLUTIONS FOR A NEW FREE-BOUNDARY PROBLEM AND IMAGE CONTOUR ENHANCEMENT", [national] Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications & Algorithms , Watam Press
Existence of Traveling Profiles Solutions to Porous Medium Equation
nonlinear differential equation, and to prove the existence and uniqueness of these new solutions under certain conditions.
Citation
M. BENHAMIDOUCHE Noureddine, (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
les mathématiques et les enjeux du developpment technologique
Citation
M. BENHAMIDOUCHE Noureddine, (2023-10-25), "les mathématiques et les enjeux du developpment technologique", [national] Mathematics and society , U.Msila - ENS Boussada
La modélisation mathématique aux service du developpment technologique
Citation
M. BENHAMIDOUCHE Noureddine, (2023-10-15), "La modélisation mathématique aux service du developpment technologique", [national] National conference on mathematics and applications , Université de Setif
THEORETICAL STUDIES ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A MULTIDIMENSIONAL NONLINEAR TIME AND SPACE-FRACTIONAL REACTION-DIFFUSION/WAVE EQUATION
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. BENHAMIDOUCHE Noureddine, (2023-05-06), "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 , Razmadze Mathematical Institute.
Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative
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. BENHAMIDOUCHE Noureddine, 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
Sur la modélisation mathématique en Biologie
Elle traite les phénomènes d'épidimiologie etc;...
Citation
M. BENHAMIDOUCHE Noureddine, (2022), "Sur la modélisation mathématique en Biologie", [national] Journnée Modélisation Mathématique en biologie , Universite de msila
Existence Of Traveling Wave Solutions For A Free Boundary Problem Of Higher-Order Space-Fractional Wave Equations
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 Schauderís and
Banachís Öxed point theorems
Citation
M. BENHAMIDOUCHE Noureddine, Rabah Djemiat, Basti Bilal, , (2022), "Existence Of Traveling Wave Solutions For A Free Boundary Problem Of Higher-Order Space-Fractional Wave Equations", [national] Applied Mathematics E-Notes, , http://www.math.nthu.edu.tw/amen
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
Citation
M. BENHAMIDOUCHE Noureddine, Rabah Djemiat, Basti Bilal, , (2022), "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, , e-ISSN: 2587-2648 Founded: 2017 Period: Quarterly Publisher: Erdal KARAPINAR
Singularités et contours
forms.
Citation
M. BENHAMIDOUCHE Noureddine, (2021), "Singularités et contours", [national] Journnée International de Mathématiques, SMA 2021. , Alger
Existence results of self similar solutions to the caputo-types space-fractional heat equation
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. BENHAMIDOUCHE Noureddine, bilal basti, , (2020), "Existence results of self similar solutions to the caputo-types space-fractional heat equation", [national] surveys in Mathematics and its applications , http:/www.utgjiu.ro/math/sma
Global Existence and Blow-up of Generalized Self-Similar Solutions to Nonlinear Degenerate Diffusion Equation Not in Divergence Form
self-similar form of the degenerate parabolic partial di§erential equation which is known as "nonlinear
di§usion equation not in divergence form". By applying the properties of Banachís Öxed point theorems,
we establish several results on the existence and uniqueness of the general form of self-similar solutions
of this equation.
Citation
M. BENHAMIDOUCHE Noureddine, Basti Bilal, , (2020), "Global Existence and Blow-up of Generalized Self-Similar Solutions to Nonlinear Degenerate Diffusion Equation Not in Divergence Form", [national] Applied Mathematics E-Notes, , http://www.math.nthu.edu.tw/amen/
Existence Results for Nonlinear Katugampola Fractional Differential Equations with an Integral Condition
nonlinear fractional di erential equations via the Katugampola fractional derivatives
with an integral condition. The arguments for the study are based upon the Banach
contraction principle, Schauder's xed point theorem, and the nonlinear alternative
of Leray-Schauder type.
Citation
M. BENHAMIDOUCHE Noureddine, Djemiat rabah, Basti Bilal, , (2020), "Existence Results for Nonlinear Katugampola Fractional Differential Equations with an Integral Condition", [national] Acta Math. Univ. Comenianae , http://www.math.nthu.edu.tw/amen/
Modèles mathématiques de contours d’image
en générale es problèmes sont mal posé, on discutera également de ce problème
Citation
M. BENHAMIDOUCHE Noureddine, (2019), "Modèles mathématiques de contours d’image", [national] la 9ème édition du colloque Tendances dans les Applications Mathématiques en Tunisie Algérie Maroc , Tlemcen
New exact solutions to nonlinear diffusion equation that occurs in image processing
Citation
M. BENHAMIDOUCHE Noureddine, Chouder Rafaa, , (2019), "New exact solutions to nonlinear diffusion equation that occurs in image processing", [national] International Journal of Computing Science and Mathematics , IJCSM - Inderscience Publishers
Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations
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. BENHAMIDOUCHE Noureddine, 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
Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola
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. BENHAMIDOUCHE Noureddine, Basti bilal, , (2019), "Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola", [national] Applied Mathematics E-Notes , Tsing Hua University Hsinchu, TAIWAN
Travelling profile solutions for nonlinear degenerate parabolic equation and contour enhancement in image processing
solutions to a nonlinear diffusion equation that occurs in image processing. Some
of these explicit solutions are related with the phenomenon of contour enhancement in image processing. We present a generalization of the results obtained by
Barenblatt to study the contour enhancement in image processing for exponent
range of parameter enhancement.
Citation
M. BENHAMIDOUCHE Noureddine, Chouder Rafaa, , (2018), "Travelling profile solutions for nonlinear degenerate parabolic equation and contour enhancement in image processing", [national] Appl. Math. E-Notes , Official Website http://www.math.nthu.edu.tw/~amen/
BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS
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. BENHAMIDOUCHE Noureddine, (2017), "BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS", [international] Surveys in Mathematics and its Applications , Bucharest University, Romania
Bayesian estimation of the self-similarity exponent of the Nile River
H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.
Citation
M. BENHAMIDOUCHE Noureddine, Benmehdi Sabah, N. Makarava, , (2011), "Bayesian estimation of the self-similarity exponent of the Nile River", [national] Nonlinear Processes in Geophysics , EGU
New Method for Constructing Exact Solutions to Nonlinear PDEs
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. BENHAMIDOUCHE Noureddine, (2009), "New Method for Constructing Exact Solutions to Nonlinear PDEs", [national] International Journal of Nonlinear Science , World Academic Press, World Academic Union, England, UK
Exact solutions to some nonlinear PDEs, travelling profile method
Citation
M. BENHAMIDOUCHE Noureddine, (2008), "Exact solutions to some nonlinear PDEs, travelling profile method", [national] Electronic Journal of Qualitative Theory of Differential Equations , Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences
Traveling Wavelets approach to the Gravitational Instability theory
Citation
M. BENHAMIDOUCHE Noureddine, Bruno Toresani, Roland Triay, , (1999), "Traveling Wavelets approach to the Gravitational Instability theory", [national] Monthly Notices of the Royal Astronomical Society , Oxford Academic