S. Manikandan, D. Vivek, K. Kanagarajan, E. M. Elsayed

The Existence and Hyers-Ulam Stability of Solution for an Impulsive Types Ambartsumian Equation Via X-Hilfer Generalized Proportional Fractional Derivative

In this paper, we investigate some existence and Ulam's type stability concepts of fixed point for a class of Ambartsumian equations with impulses via X-Hilfer generalized proportional fractional derivative (PFD). Our results are obtained by using standard fixed point theorems.

Mathematics Subject Classification: 26A33, 34A08, 47D09, 47H10, 93C43

Key words and phrases: Ambartsumian equation, impulsive, proportional fractional derivative, existence, uniqueness, Ulam-Hyers-Rassias stability