Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative

Abstract

By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractional derivative and integral with a weighted term. Furthermore, by dint of Schaefer’s fixed point theorem, $α$-$\psi$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples to make our main conclusion clear.