On existence results for hybrid \(\psi-\)Caputo multi-fractional differential equations with hybrid conditions

Abstract

In this paper, we study the existence and uniqueness results of a fractional hybrid boundary value problem with multiple fractional derivatives of \(\psi-\)Caputo with different orders. Using a useful generalization of Krasnoselskii’s fixed point theorem, we have established results of at least one solution, while the uniqueness of solution is derived by Banach's fixed point. The last section is devoted  to an example that illustrates the applicability of our results.