Browsing by Author "Adjabi, Y."

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Citation - WoS: 20
Citation - Scopus: 24
A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives
(Springer, 2020) Baleanu, D.; Baleanu, Dumitru; Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; 56389; Matematik
In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.
Citation - Scopus: 2
On abstract Cauchy problems in the frame of a generalized Caputo type derivative
(DergiPark, 2023) Jarad, Fahd; Bourchi, S.; Jarad, F.; Abdeljawad, Thabet; Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; 234808; Matematik
In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results. © 2023, DergiPark. All rights reserved.
Citation - WoS: 117
Citation - Scopus: 121
On Cauchy problems with Caputo Hadamard fractional derivatives
(Eudoxus Press, Llc, 2016) Jarad, Fahd; Adjabi, Y.; Baleanu, Dumitru; Jarad, Fahd; Baleanu, D.; Abdeljawad, Thabet; Abdeljawad, T.; 234808; Matematik
The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.