Ulam–Hyers stability of pantograph fractional stochastic differential equations

Lassaad Mchiri, Abdellatif Ben Makhlouf, Hafedh Rguigui

2022Mathematical Methods in the Applied Sciences22 citationsDOI

Abstract

In this paper, we investigate the existence and uniqueness theorem (EUT) of Pantograph fractional stochastic differential equations (PFSDE) using the Banach fixed point theorem (BFPT). We show the Ulam–Hyers stability (UHS) of PFSDE by the generalized Gronwall inequalities (GGI). We illustrate our results by two examples.

Topics & Concepts

MathematicsPantographGronwall's inequalityUniquenessFixed-point theoremBanach fixed-point theoremStability (learning theory)Mathematical analysisStochastic differential equationApplied mathematicsDifferential equationPicard–Lindelöf theoremFractional calculusInequalityComputer scienceMechanical engineeringMachine learningEngineeringNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFunctional Equations Stability Results