Existence, Uniqueness and Stability of Implicit Switched Coupled Fractional Differential Equations of ψ$\boldsymbol{\psi}$-Hilfer Type

Abstract

In this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results.

On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals

“…In fact, stability of physical phenomena has an old history, and one can find a lot of works in the literature not only in the last century but also before it [27][28][29][30][31][32][33][34][35][36]. During recent decades, considerable attention has been given to the study of the Hyers-Ulam stability of functional differential and integral equations [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54].…”

Discrete fractional order two-point boundary value problem with some relevant physical applications

“…These equations, which involve derivatives or integrals of fractional order, have resulted in a great interest for many researchers due to their effective applications in physics, chemistry, chaotic dynamical systems and random walks with memory in different fields of applied mathematics and engineering. Particularly emphasis has been put to the topics on existence, uniqueness and stability of solutions of differential equations of fractional order; see [13][14][15][16][17][18][19][20][21][22][23][24][25] and the references cited therein. The corresponding discrete counter part, fractional order difference equations (FODEs), have appeared as a new research area for mathematicians and scientists.…”

Well‐posedness and Hyers‐Ulam results for a class of impulsive fractional evolution equations

“…Wang et al 25 are the first mathematician who investigated the Ulam‐type stability and data dependence for FDE. For the detailed study of Ulam‐type stability, we recommend other studies 13,14,24,26‐34 …”

“…For the detailed study of Ulam-type stability, we recommend other studies. 13,14,24,[26][27][28][29][30][31][32][33][34] Recently, Sutar and Kucche 35 studied the following impulsive FDE:…”