Qualitative Analysis of Langevin Integro-Fractional Differential Equation under Mittag–Leffler Functions Power Law
Mohammed A. Almalahi, F. Ghanim, Thongchai Botmart, Omar Bazighifan, Sameh Askar
Abstract
This research paper intends to investigate some qualitative analysis for a nonlinear Langevin integro-fractional differential equation. We investigate the sufficient conditions for the existence and uniqueness of solutions for the proposed problem using Banach’s and Krasnoselskii’s fixed point theorems. Furthermore, we discuss different types of stability results in the frame of Ulam–Hyers by using a mathematical analysis approach. The obtained results are illustrated by presenting a numerical example.
Topics & Concepts
UniquenessMathematicsLangevin equationFixed-point theoremStability (learning theory)Frame (networking)Qualitative analysisApplied mathematicsDifferential equationBanach spaceMathematical analysisStatistical physicsComputer sciencePhysicsQualitative researchMachine learningSociologyTelecommunicationsSocial scienceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results