A Class of Implicit Fractional $\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space

Abstract

The aim of this work is to find the Ulam-Hyers-Rassias stability and investigate the existence and uniqueness of solutions for a class of implicit fractional $\psi$-Hilfer Langevin equation with impulse and time delay. A novel form of generalized Gronwall inequality is introduced. We utilize these findings together with Picard operator theory in our analysis. An example will be given to support the validity of our findings.