Existence and Ulam stability of solution to fractional order hybrid differential equations of variable order

Norravich Limpanukorn, Parinya Sa Ngiamsunthorn

Abstract

In this paper we study fractional hybrid differential equation of variable order ${0}<\alpha(t)\leq{1}$ in the sense of Caputo. The existence of solution is proved by Krasnoselkii fixed point theorem. In addition, we study stability of solutions in the sense of Ulam-Hyers stability. Finally, an example is given to illustrate the result.