Fractional order iterative boundary value problem

Abstract

In the present paper, we establish the existence and uniqueness solution for an iterative differential equation involving caputo fractional derivative of order $1<\alpha<2$. The existence results is proved by using Schauder fixed point. To prove the extremal solution, we demonstrate some fractional inequalities. As application, we conclude this paper by giving an illustrative example to demonstrate the applicability of the obtained result.