Common fixed point theorems for auxiliary functions with applications in fractional differential equation

Abstract

Abstract In this work, we investigate h-ϕ contraction mappings with two metrics endowed with a directed graph which involve auxiliary functions. The achievement allows us to obtain applications for the existence of the solutions for Caputo fractional boundary value problems with the integral boundary condition type. In addition, we also give examples and numerical experiments supporting our main results.

Keywords

• Fixed point
• Common fixed point
• Fractional differential equation