Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Dongdong Gao () and Jianli Li
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Dongdong Gao: Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China
Jianli Li: College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Mathematics, 2024, vol. 12, issue 8, 1-16

Abstract: In this paper, we study the existence, uniqueness and Hyers–Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer’s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers–Ulam stable via Gronwall’s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

Keywords: Hyers–Ulam stability; Caputo fractional derivative; random impulses; Schaefer’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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