New Existence and Stability Results for ψ,w-Caputo−Fabrizio Fractional Nonlocal Implicit Problems

In the context of ψ-weighted Caputo−Fabrizio fractional derivatives, we develop and extend the existence and Ulam−Hyers stability results for nonlocal implicit differential equations. The fixed-point theorems due to Banach and Krasnoselskii are the foundation for the proof of existence and uniqueness results. Additionally, the Ulam−Hyers stability demonstrates the assurance of the existence of solutions via Gronwal inequality. Also, we offer an example as an application to explain and validate the acquired results. Finally, in terms of our outcome, we designate a more general problem for the ψ,w-Caputo−Fabrizio fractional system that includes analogous problems to the problem at hand.