Stability Analysis of Implicit Fractional Differential Equations with Hilfer-Katugampola Derivatives

Abstract

This paper aims to investigate nonlinear implicit differential equation(DEs) using the fractional derivative(FD) of Hilfer-Katugampola(H-K). The presence of the implicit equation’s solution is established through the application of the Gronwall inequality and the Banach f ixed point theorem, leading to pertinent findings regarding Ulam Hyers stability(UHS). Lastly, an example confirms that the findings are valid.