Existence and stability of a Caputo variable-order boundary value problem (Q2051703)

Summary: In this study, we investigate the existence of a solution to the boundary value problem (BVP) of variable-order Caputo-type fractional differential equation by converting it into an equivalent standard Caputo (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All our results in this study are proved by using Darbo's fixed-point theorem and the Ulam-Hyers (UH) stability definition. A numerical example is given at the end to support and validate the potentiality of our obtained results.