Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative (Journal of Nonlinear Modeling and Analysis, 2024)
By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractionalderivative and integral with a weighted term. Furthermore, by dint of Schaefer’s fixed point theorem, $α$-$ψ$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples tomake our main conclusion clear.
Keywords: Higher-order weighted fractional derivative; Caputo-Fabrizio derivative; existence.