On the qualitative analysis of the boundary value problem of the Ψ-Caputo implicit fractional pantograph differential equation

In this manuscript, the primary objective is to analyze a Ψ-Caputo fractional pantograph implicit differential equation using the Ψ-Caputo fractional derivative. We employ a newly developed method based on fixed-point theorems to explore the existence and uniqueness of the solution to our proposed problem. Furthermore, we investigate the stability of the proposed problem. Finally, we provide an example that illustrates the application of our newly obtained results, confirming their practical significance.