Some results of the nonlinear hybrid fractional differential equations in Banach algebra

Abstract

In this paper, a fixed point theorem of Dhage is used to prove under mixed Lipschitz and Caratheodory conditions the existence of solutions for a nonlinear hybrid fractional differential equation in Banach algebra with two-point integral hybrid boundary conditions. Furthermore, sufficient conditions for existence and uniqueness of mild solutions are derived. In addition, the Ulam-Hyers types of stability of solutions are established. Finally, a numerical example is given to clarify the acquired outcomes.