Existence and Hyers–Ulam Stability for a Multi-Term Fractional Differential Equation with Infinite Delay
Chen Chen, Qixiang Dong
Abstract
This paper is devoted to investigating one type of nonlinear two-term fractional order delayed differential equations involving Caputo fractional derivatives. The Leray–Schauder alternative fixed-point theorem and Banach contraction principle are applied to analyze the existence and uniqueness of solutions to the problem with infinite delay. Additionally, the Hyers–Ulam stability of fractional differential equations is considered for the delay conditions.
Topics & Concepts
MathematicsUniquenessFixed-point theoremContraction principleContraction mappingFractional calculusTerm (time)Nonlinear systemBanach fixed-point theoremMathematical analysisDifferential equationDelay differential equationApplied mathematicsStability (learning theory)Type (biology)Banach spaceSchauder fixed point theoremPicard–Lindelöf theoremComputer sciencePhysicsMachine learningBiologyEcologyQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations