Hyers–Ulam Stability and Existence of Solutions to the Generalized Liouville–Caputo Fractional Differential Equations
Kui Liu, Mičhal Fĕckan, JinRong Wang
Abstract
The aim of this paper is to study the stability of generalized Liouville–Caputo fractional differential equations in Hyers–Ulam sense. We show that three types of the generalized linear Liouville–Caputo fractional differential equations are Hyers–Ulam stable by a ρ -Laplace transform method. We establish existence and uniqueness of solutions to the Cauchy problem for the corresponding nonlinear equations with the help of fixed point theorems.
Topics & Concepts
MathematicsUniquenessLaplace transformStability (learning theory)Mathematical analysisNonlinear systemFractional calculusCauchy distributionDifferential equationInitial value problemType (biology)Fixed-point theoremApplied mathematicsComputer sciencePhysicsEcologyQuantum mechanicsMachine learningBiologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results