MB
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1
D_{0+}^{alpha} u(t) + f(t,u(t)) = 0
I_{0+}^{alpha} f(t) = (1/Γ(α)) ∫_0^t (t-s)^{α-1} f(s) ds
^{C}D^{α} u(t)
u(0)=u'(0)=0, u'(1)=μ u'(η)
Γ(α)Γ(1-α)=π/sin(πα)
||Tu-Tv|| ≤ k||u-v||, 0<k<1

Publications

54 items
2025

Solvability of the system involving the mixed derivative and integral Erd´ elyi-Kober equations of fractional order

Abdallah Djaout, Maamar Benbachir, Mohammad Esmael Samei, Mustapha Lakrib.

Journal of Inequalities and ApplicationsDOI: 10.1186/s13660-025-03383-7
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2025

New Existence and Stability Results of a Backward Impulsive FDEs

Nabila Benahmed, Maamar Benbachir, Farid Chabane, Mohammad Esmael Samei.

2024

On the ρ-Caputo Impulsive p-Laplacian Boundary Problem: An Existence Analysis

Farid Chabane, Maamar Benbachir, Sina Etemad, ˙Ibrahim Avcı.

Qualitative Theory of Dynamical Systems
2024

On solution of non-linear FDE under tempered Ψ-Caputo derivative for the first-order and three-point boundary conditions

Kamel Bensassa, Maamar Benbachir, Mohammad Esmael Samei, Soheil Salahshour.

BULLETIN OF THE KARAGANDA UNIVERSITYMATHEMATICS
2023

Solvability and stability analysis of a coupled system involving generalized fractional derivatives

Djaout Abdellah, Maamar Benbachir, Mustapha Lakrib, Thabet Abdeljawad.

AIMS Mathematics
2023

Advances in Computational Mathematics and Modelling on the Solvability of Time Conformable Fractional Equation Set on Singular Domain of Rn+1

Chaouchi Belkacem, Maamar Benbachir, Marko Kosti´ c.

2023

Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals

Tahar Kherraz, Maamar Benbachir, Mustapha Lakrib, Shailesh A. Bhanotar.

Chaos Solitons & Fractals
2022

Blowing-up solutions for time-fractional equations on a bounded domain

Abdelatif Boutiara, Mohammed K A Kaabar, Maamar Benbachir, Xiao-Guang Yue.

Advances in Mechanical Engineering
2022

Existence and Uniqueness Results for a Fractional Boundary Value Problems with Multiple Orders of Fractional Derivatives and Integrals

Tahar Kherraz, Maamar Benbachir, Mustapha Lakrib, Shailesh A. Bhanotar.

SSRN Electronic Journal
2022

Analysis of a fractional boundary value problem involving Riesz-Caputo fractional derivative

A. Boutiara, N. Adjimi, M. Benbachir, M.S. Abdo

Advances in the Theory of Nonlinear Analysis and its Applications
2022

Existence of positive solutions for p-Laplacian boundary value problems of fractional differential equations

Farid Chabane, Maamar Benbachir, Mohamed Hachama, Mohammad Esmael Samei.

Boundary Value ProblemsDOI: 10.1186/s13661-022-01645-7
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2022

Some Further Refinements Of Hermite-Hadamard Type Inequalities For Harmonically Convex And P-Convex Functions Via Fractional Integrals

Maamar Benbachir, Farid Chabane, ˙Imdat ˙I¸ scan.

Iranian Journal of Mathematical Sciences and Informatics
2022

Successive Approximations for Caputo-Fabrizio Fractional Differential Equations

Fatima Si Bachir, Sa¨ ıd Abbas, Maamar Benbachir, Mouffak Benchohra.

Tatra Mountains Mathematical Publications
2022

Existence Solutions for a Nonlinear Langevin Fractional q-Difference System in Banach Space

Abdelatif Boutiara, Maamar Benbachir, Mansour Saleman M. Lotayif.

Progress in Fractional Differentiation and Applications
2021

Solvability for multi-point BVP of nonlinear fractional differential equations at resonance with three dimensional kernels

Z. Baitiche, M. Benbachir, K. Guerbati

Kragujevac Journal of Mathematics
2021

Hilfer Fractional Hybrid Differential Equations with Multi-point Boundary Hybrid Conditions

A. Boutiara, M. Benbachir, K. Guerbati

International Journal of Modern Mathematical Sciences
2021

Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψCaputo Fractional Boundary Value Problem

Abdelatif Boutiara, Maamar Benbachir, Jehad Alzabut, Mohammad Esmael Samei.

Fractal Fract
2021

Kuratowski MNC method on a generalized fractional Caputo Sturm-Liouville-Langevin q-difference problem with generalized Ulam-Hyers stability

Abdelatif Boutiara, Maamar Benbachir, Sina Etemad, Shahram Rezapour.

Advances in Difference Equations
2021

Existence and attractivity results for ψ-Hilfer hybrid fractional differential equations

Fatima Si Bachir, Sa¨ ıd Abbas, Maamar Benbachir, Gaston M. N’Gu´ er´ ekata.

Cubo (Temuco)
2021

Existence of Concave Positive Solutions for Nonlinear Fractional Differential Equation with p-Laplacian Operator

F. Farid, S. Abbas, M. Benbachir, M. Benchohra, G.M. N’Gu´ er´ ekata

Vietnam Journal of Mathematics
2021

Successive approximations for random coupled Hilfer fractional differential systems

F. Si Bachir, S. Abbas, M. Benbachir, M. Benchohra

Arabian Journal of Mathematics
2021

Existence results for nonlinear neutral generalized Caputo fractional differential equations

N. Adjimi, A. Boutiara, M.S. Abdo, M. Benbachir

Journal of Pseudo-Differential Operators and Applications
2021

Existence results and Ulam-Hyers stability to impulsive coupled system fractional differential equations

B. Hadjer, M. Benbachir

Turkish Journal of Mathematics
2021

Existence results for ψ-Caputo hybrid fractional integro-differential equations

N. Adjimi, M. Benbachir, K. Guerbati

Malaya Journal of Matematik
2021

Katugampola Fractional Differential Equation with Erd´ elyiKober Integral Boundary Conditions

N. Adjimi, M. Benbachir

Advances in the Theory of Nonlinear Analysis and its Applications
2021

Hilfer-Hadamard fractional differential equations; Existence and Attractivity

F. Si Bachir, S. Abbas, M. Benbachir, M. Benchohra

Advances in the Theory of Nonlinear Analysis and its Application
2021

Implicit fractional differential equation involving ψ-Caputo with boundary conditions

A. Boutiara, M. Benbachir

Bulletin of the Institute of Mathematics Academia Sinica New Series
2021

Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

H. Belbali, M. Benbachir

Journal of Mathematical Modeling
2020

Solvability of two-point fractional boundary value problems at resonance

Z. Baitiche, M. Benbachir, K. Guerbati

Malaya Journal of Matematik
2020

Hilfer-Hadamard Fractional Differential Equations; Existence and Attractivity

Fatima Si Bachir, Sa¨ ıd Abbas, Maamar Benbachir, Mouffak Benchohra.

Advances in the Theory of Nonlinear Analysis and its Application
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2020

Caputo Type Fractional Differential equation With Nonlocal Erd´ elyi-Kober type Integral Boundary Conditions In Banach spaces

A. Boutiara, M. Benbachir, K. Guerbati

Surveys in Mathematics and its Applications
2020

Measure of noncompactness for nonlinear Hilfer fractional differential equation with nonlocal Riemann-Liouville integral boundary conditions in Banach spaces

Abdelatif Boutiara, Maamar Benbachir, Kaddour Guerbati.

Open Journal of Mathematical Sciences
2020

Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

Belbali Hadjer, Maamar Benbachir.

2019

Measure Of Noncompactness For Nonlinear Hilfer Fractional Differential Equation In Banach Spaces

A. Boutiara, M. Benbachir, K. Guerbati

Ikonion Journal of Mathematics
2019

Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces

A. Boutiara, M. Benbachir, K. Guerbati

AIMS Mathematics
2019

Application of a generalization of Miranda’s theorem for solutions of two-point BVP of nonlinear fractional differential equations at resonance

Z. Baitiche, M. Benbachir, K. Guerbati

Canadian Journal of Applied Mathematics
2018

An existence and uniqueness result for nth-order nonlinear fractional differential equations

A. Benlabbes, M. Benbachir, M. Lakrib

International Journal of Nonlinear Analysis and Applications
2015

Existence solutions for three point boundary value problem for differential equations

M. Houas, M. Benbachir

Journal of Fractional Calculus and Applications
2015

Existence solutions for four point boundary value problems for fractional differential equations

M. Houas, M. Benbachir

Pure and Applied Mathematics Letters
2015

Some Results for a Four-Point Boundary Value Problems for Coupled System involving Caputo Derivative

M. Houas, M. Benbachir, Z. Dahmani

Malaya Journal of Matematik
2015

Existence and Uniqueness Results For a Nonlinear Differential Equations of Arbitrary Order

M. Houas, M. Benbachir

International Journal of Nonlinear Analysis and Applications
2015

Boundary value problems for nonlinear fractional differential equations

A. Benlabbes, M. Benbachir, M. Lakrib

FACTA UNIVERSITATIS (NIS)
2014

Existence solutions of nonlinear fractional differential equations

A. Benlabbes, M. Benbachir, M. Lakrib

Journal of Advanced Research in Dynamical and Control Systems
2014

The Kawahara Equation With Time and Space-Fractional Derivatives Solved by The Adomian Method

M. Benbachir, A. Saadi

Journal of Interdisciplinary Mathematics
2013

New results for a boundary value problem for differential equations of arbitrary order

M. Houas, Z. Dahmani, M. Benbachir

International Journal of Modern Mathematical Sciences
2013

An Extension of Hermite-Hadamard inequality for symmetrized convex function

A. El Farissi, M. Benbachir, M. Dahmane

Real Analysis Exchange
2013

Anti-periodic boundary value problems

Boundary Value Problems

Boundary Value ProblemsDOI: 10.1186/1687-1847-2013-306
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2013

Oscillation of fixed points of solutions of some linear differential equations

A. El Farissi, M. Benbachir

Electronic Journal of Differential Equations
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2012

Positive solutions to three-point nonlinear fractional semi-positone boundary

A. Saadi, A. Benmezai, M. Benbachir

PanAmerican Mathematical Journal
2011

The ADM Method For Solving the Modified Kawahara Equation With Fractional Spatial and Temporal Derivatives

M. Benbachir, Z. Dahmani

Journal of Interdisciplinary Mathematics
2011

Positive solutions for three-point nonlinear fractional boundary value problems

A. Saadi, M. Benbachir

Electronic Journal of Qualitative Theory of Differential Equations
2010

Slow and fast systems with Hamiltonian reduced problems

M. Benbachir, K. Yadi, R. Bebbouchi

Electronic Journal of Differential Equations
2009

Numerical solution of the coupled Burgers equations with time and space fractional derivatives

A. Saadi, M. Benbachir

Annals de l’Universit´ e de Bechar No. 5
2009

Solutions of the Cahn-Hilliard Equation with Time-and SpaceFractional Derivatives

Z. Dahmani, M. Benbachir

International Journal of Nonlinear Science