Stability of Ulam–Hyers and Ulam–Hyers–Rassias for a class of fractional differential equations
Qun Dai, Ruimei Gao, Zhe Li, Changjia Wang
Abstract
Abstract In this paper, we investigate a class of nonlinear fractional differential equations with integral boundary condition. By means of Krasnosel’skiĭ fixed point theorem and contraction mapping principle we prove the existence and uniqueness of solutions for a nonlinear system. By means of Bielecki-type metric and the Banach fixed point theorem we investigate the Ulam–Hyers and Ulam–Hyers–Rassias stability of nonlinear fractional differential equations. Besides, we discuss an example for illustration of the main work.
Topics & Concepts
MathematicsFixed-point theoremNonlinear systemUniquenessContraction principleBanach fixed-point theoremMathematical analysisOrdinary differential equationBanach spacePicard–Lindelöf theoremFixed pointContraction mappingPartial differential equationClass (philosophy)Stability (learning theory)Applied mathematicsDifferential equationComputer scienceQuantum mechanicsMachine learningPhysicsArtificial intelligenceFunctional Equations Stability ResultsNonlinear Differential Equations AnalysisFractional Differential Equations Solutions