Abstract
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).
Highlights
It has been observed that the focus of investigation has shifted from classical integer-order models to fractional-order models
It is because of the fact that many practical systems are excellently described by using fractional-order differential equations (FODEs) instead of classical differential equations
E study of implicit systems of FODEs with impulsive conditions is quite important as such systems appear in a variety of problems of applied nature, especially in biosciences, economics, engineering, etc
Summary
It has been observed that the focus of investigation has shifted from classical integer-order models to fractional-order models. E study of implicit systems of FODEs with impulsive conditions is quite important as such systems appear in a variety of problems of applied nature, especially in biosciences, economics, engineering, etc. Boundary and initial conditions may be local or nonlocal and both are important, and increasingly many problems have been investigated under these conditions. Gupta and Dabas [17] studied the existence and uniqueness results for a class of IFODEs with nonlocal boundary conditions. Is paper can be considered as generalization of the aforesaid work, in which we discuss existence, uniqueness, and various stability results for the following implicit IFODEs with three point NCFBCs of order ρ ∈ E further organization of this manuscript is divided into four parts as follows: e second part of the paper demonstrates the preliminary portion in which we recall to readers the basics of used theory, notations, and definitions. e third part presents an existence result by employing Schaefer’s fixed point theorem. e fourth section is introduced to analyze and study several stability results of the considered problem, and the last section is provided to illustrate the applications of the obtained results
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