Boundary value problem of Caputo fractional differential equations of variable order

Abstract

In this work, we investigate the existence, uniqueness and the stability of solutions to the boundary value problem (BVP) of Caputo fractional differential equations of variable order by converting it into an equivalent standard Caputo BVP of the fractional constant order with the help of the generalized intervals and piecewise constant functions. The results obtained in this interesting study are novel and worthy based on the Krasnoselskii fixed point theorem and the Banach contraction principle. The Ulam-Hyers stability of the given variable-order Caputo fractional boundary value problem is established. A numerical examples is given at the end to support and validate the potentiality of our obtained results.