Using Krasnoselskii's theorem to investigate the Cauchy and neutral fractional q-integro-differential equation via numerical technique

Abstract

This article discusses the stability results for solution of a fractional q-integro-differential problem via integral conditions. Utilizing the Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on the results obtained, conditions are provided to ensure the generalized Ulam and Ulam–Hyers–Rassias stabilities of the original system. The results are illustrated by two examples.

Keywords

• nonlinear fractional integro-differential equation
• neutral differential equation
• cauchy differential equation
• existence and stability
• 34a08
• 34b16
• 39a13