On boundary value problems of Caputo fractional differential equation of variable order via Kuratowski MNC technique

Abstract

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.