Processing Fractional Differential Equations Using ψ-Caputo Derivative

Recently, many scientists have studied a wide range of strategies for solving characteristic types symmetric differential equations, including fractional equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness solutions (EUS) FDEs in sense ψ-Caputo derivative (ψ-CFD) second-order 1<α<2. We know that ψ-CFD is generalization previously familiar derivatives: Riemann-Liouville Caputo. By applying Banach fixed-point theorem (BFPT) Schauder (SFPT), desired results, embody theoretical results obtained, provided two examples illustrate proofs.