Browsing by Author "Benchohra, M."

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Citation - Scopus: 5
Advanced Topics in Fractional Differential Equations A Fixed Point Approach
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
Citation - Scopus: 4
Coupled Systems for Fractional Differential Equations
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
This chapter deals with some existence and uniqueness results for a class of coupled systems for nonlinear k-generalized ψ -Hilfer fractional differential equations with boundary and terminal conditions. Our results are based on some necessary fixed point theorems. Furthermore, an illustration is presented for each section to demonstrate the plausibility of our results. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 6
Fractional Differential Equations with Instantaneous Impulses
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
The aim of this chapter is to prove some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer-type fractional derivative. We base our arguments on some relevant fixed point theorems combined with the technique of measure of noncompactness. Examples are included to show the applicability of our results for each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 3
Fractional Differential Equations with Non-Instantaneous Impulses
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
The present chapter deals with some existence, uniqueness, and Ulam stability results for a class of initial and boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer-type fractional derivative. The tools employed are some suitable fixed point theorems combined with the technique of measure of noncompactness. We provide illustrations to demonstrate the applicability of our results for each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 4
Fractional Differential Equations with Retardation and Anticipation
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
In this chapter, we prove some existence and uniqueness results for a class of boundary and terminal value problems for implicit nonlinear k-generalized ψ -Hilfer fractional differential equations involving both retarded and advanced arguments. Further, examples are given to illustrate the viability of our results in each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 6
Hybrid Fractional Differential Equations
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
This chapter is devoted to proving some results concerning the existence of solutions for a class of initial and boundary value problems for nonlinear fractional Hybrid differential equations and Generalized Hilfer fractional derivative. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 11
Implicit Fractional Differential Equations
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
This chapter deals with some existence and Ulam stability results for a class of initial and boundary value problems for differential equations with generalized Hilfer-type fractional derivative in Banach spaces. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 2
Impulsive Fractional Differential Equations with Retardation and Anticipation
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
This chapter deals with the existence and uniqueness results for a class of impulsive initial and boundary value problems for implicit nonlinear fractional differential equations and k-Generalized ψ -Hilfer fractional derivative involving both retarded and advanced arguments. Our results are based on some necessary fixed point theorems. Suitable illustrative examples are provided for each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 0
Introduction
(Springer Nature, 2023) Benchohra, M.; Karapınar, E.; Lazreg, J.E.; Salim, A.
Fractional calculus is an area of mathematical analysis that extends the concepts of integer differential calculus to involve real or complex order derivatives and integrals. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 0
Introduction
(Springer Nature, 2023) Benchohra, M.; Karapınar, E.; Lazreg, J.E.; Salim, A.
Fractional calculus is a field in mathematical analysis which is a generalization of integer differential calculus that involves real or complex order derivatives and integrals [10–14, 25, 28, 43, 50–52]. There is a long history of this concept of fractional differential calculus. One might wonder what meaning could be attributed to the derivative of a fractional order, that is dnydxn, where n is a fraction. Indeed, in correspondence with Leibniz, L’Hopital considered this very possibility. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 1
Nonlocal partial fractional evolution equations with state dependent delay
(Universidad Catolica del Norte, 2023) Lachachi-Merad, N.; Karapınar, Erdal; Baghli-Bendimerad, S.; Benchohra, M.; Karapınar, E.; 19184; Matematik
In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions. © (2023), (SciELO-Scientific Electronic Library Online). All Rights Reserved.
Citation - Scopus: 0
Preface
(Springer Nature, 2023) Benchohra, M.; Karapınar, E.; Lazreg, J.E.; Salim, A.
Citation - Scopus: 0
Preliminary Background
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
In this chapter, we discuss the necessary mathematical tools, notations, and concepts we need in the succeeding chapters. We look at some essential properties of fractional differential operators. We also review some of the basic properties of measures of noncompactness and fixed point theorems which are crucial in our results regarding fractional differential equations. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.