A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions

Abstract

In this paper, we introduce a new kind of generalized fractional integral boundary conditions and develop the existence theory for a fractional di erential equation involving generalized Caputotype fractional derivative equipped with these conditions. We also study the inclusion case of the given problem. Examples are constructed to demonstrate the application of the obtained results.

Keywords

• differential equations and inclusion
• generalized Caputo derivative
• fractional integral
• existence
• fixed point