Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition

Abstract

Abstract In this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented.

Keywords

• Fractional inclusion problem
• Hilfer and Erdélyi–Kober fractional operators
• Existence
• Fractional integral boundary conditions
• Convex
• Nonconvex