Existence of solution for some nonlinear g-Caputo fractional-order differential equations based on Wardowski–Mizoguchi–Takahashi contractions

Abstract

Abstract In this study, we prove the existence and uniqueness of a solution to a g-Caputo fractional differential equation with new boundary value conditions utilizing the combined Wardowski–Mizoguchi–Takahashi contractions via reduction of this equation to a fractional integral equation. We provide an example to demonstrate our findings.

Keywords

• Fixed point
• Fractional integral equation (FIE)
• g-Caputo fractional differential equation
• Wardowski contraction
• Mizoguchi–Takahashi contraction