Analysis of generalized fractional differential equations and inclusions with non-local generalized fractional integral boundary conditions

Abstract

This paper is concerned with the existence of results for boundary value problems involving nonlinear generalized fractional differential equations and inclusions with non-local generalized fractional integral boundary conditions. The existence results for equations depends on the O’Regan’s fixed point theorem and Banach fixed point theorem. Besides, the existence results for inclusion depends on the nonlinear alternative for contractive maps. Examples are provided to demonstrate the feasibility of the obtained results, and also we have discussed some variates of the given problem.