Browsing by Author "Ali, Arshad"

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Citation - WoS: 38
Citation - Scopus: 55
Existence and Stability Analysis To a Coupled System of Implicit Type Impulsive Boundary Value Problems of Fractional-Order Differential Equations
(Springer, 2019) Jarad, Fahd; Gupta, Vidushi; Abdeljawad, Thabet; Ali, Arshad; Shah, Kamal
In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to obtain conditions for the existence and uniqueness of positive solutions. We discuss Hyers-Ulam (HU) type stability of the concerned solutions and provide an example for illustration of the obtained results.
Citation - WoS: 8
Citation - Scopus: 11
Mathematical Analysis of Nonlocal Implicit Impulsive Problem Under Caputo Fractional Boundary Conditions
(Hindawi Ltd, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; Ali, Arshad; Gupta, Vidushi
This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).
Citation - WoS: 17
Citation - Scopus: 26
Ulam-Hyers Stability Analysis To a Class of Nonlinear Implicit Impulsive Fractional Differential Equations With Three Point Boundary Conditions
(Springer, 2019) Ali, Arshad; Shah, Kamal; Jarad, Fahd; Asma
In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equations. Using classical fixed point theorems, we develop the required conditions. Further, using the techniques of nonlinear functional analysis, we investigate Ulam-Hyers stability results to the proposed problem. For applications of our derived results, we present two numerical examples.