Browsing by Author "Souid, Mohammed Said"

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Boundary value problem for nonlinear fractional differential equations of variable order via Kuratowski MNC technique
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Souid, Mohammed Said; Hakem, Ali; İnç, Mustafa; 56389
In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo's fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.
Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order
(2023) Jarad, Fahd; Abdeljawad, Thabet; Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; 234808
This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam–Hyers–Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results. © 2023, Springer Nature Switzerland AG.
On boundary value problems of Caputo fractional differential equation of variable order via Kuratowski MNC technique
(2022) Jarad, Fahd; Souid, Mohammed Said; Jarad, Fahd; Hakem, Ali; 234808
In this manuscript, we examine both the existence and the stability of solutions to the boundary value problem of Caputo fractional differential equations of variable order by converting it into an equivalent standard Caputo boundary value problem of the fractional constant order with the help of the generalized intervals and the piece-wise constant functions. All results in this study are established using Darbo’s fixed point theorem combined with the Kuratowski measure of noncompactness. Further, the Ulam–Hyers stability of the given problem is examined; and finally, we construct an example to illustrate the validity of the observed results.
On the boundary value problems of Hadamard fractional differential equations of variable order
(2023) Benkerrouche, Amar; Souid, Mohammed Said; Karapinar, Erdal; Hakem, Ali; 19184
In this manuscript, we examine both the existence, uniqueness, and the stability of solutions to the boundary value problem (BVP) of Hadamard fractional differential equations of variable order by converting it into an equivalent standard Hadamard (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All results in this study are established using Krasnoselskii fixed-point theorem and the Banach contraction principle. Further, the Ulam–Hyers stability of the given problem is examined, and finally, we construct an example to illustrate the validity of the observed results.