Qualitative results for Iterative fractional differential equations with mixed boundary conditions

Abstract

This paper is about existence and uniqueness results of iterative fractional differential equations with mixed fractional derivative equipped with integral boundary condition. We establish an important equivalence between our problem and a homogeneous integral equation. Using Banach fixed point theorem and Krasnoselskii fixed point theorem, existence and uniqueness of solutions for our problem is proved. Further, Various Ulam-Hyers stability results are studied which are further explained by applying the results to examples.