Some existence results for a differential equation and an inclusion of fractional order via (convex) F-contraction mapping

Abstract

Abstract The existence of solutions for a class of μ-Caputo fractional differential equations and an inclusion problem equipped with nonlocal μ-integral boundary conditions are investigated. We use F-contraction, convex F-contraction, and some consequences to achieve the desired goals. Finally, some examples are provided to illustrate the results.

Keywords

• Convex F-contraction
• Fixed point
• Fractional differential inclusion