Browsing by Author "Shah, K."

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Citation - Scopus: 0
Existence of Solutions of Multi-Order Fractional Differential Equations
(Elsevier B.V., 2025) Bouchelaghem, F.; Boulares, H.; Ardjouni, A.; Jarad, F.; Abdeljawad, T.; Abdalla, B.; Shah, K.
Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings. © 2025
Citation - WoS: 81
Citation - Scopus: 82
On the weighted fractional operators of a function with respect to another function
(World Scientific Publ Co Pte Ltd, 2020) Jarad, Fahd; Jarad, F.; Abdeljawad, T.; Abdeljawad, Thabet; Shah, K.; 234808; Matematik
The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.
Citation - WoS: 21
Citation - Scopus: 36
Study on Krasnoselskii's fixed point theorem for Caputo-Fabrizio fractional differential equations
(Springer, 2020) Eiman; Baleanu, Dumitru; Shah, K.; Sarwar, M.; Baleanu, D.; 56389; Matematik
This note is concerned with establishing existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative. By using usual classical fixed point theorems of Banach and Krasnoselskii, we develop sufficient conditions for the existence of at least one solution and its uniqueness. Further, some results about Ulam-Hyers stability and its generalization are also discussed. Two suitable examples are given to demonstrate the results.
Citation - WoS: 16
Citation - Scopus: 23
Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations
(Springer, 2019) Ali, A.; Baleanu, Dumitru; Shah, K.; Baleanu, D.; 56389; Matematik
In this paper, we derive some sufficient conditions which ensure the existence and uniqueness of a solution for a class of nonlinear three point boundary value problems of fractional order implicit differential equations (FOIDEs) with some boundary and impulsive conditions. Also we investigate various types of Hyers-Ulam stability (HUS) for our concerned problem. Using classical fixed point theory and nonlinear functional analysis, we obtain the required conditions. In the last section we give an example to show the applicability of our obtained results.