Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative
Ho Vu, John Michael Rassias, Ngo Van Hoa
Abstract
The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP‐FDEs) via the concept of Caputo fractional derivative with respect to another function with the order . The existence and uniqueness results of a solution for BVP‐FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide new sufficient conditions to guarantee the Hyers‐Ulam stability and the Hyers–Ulam–Rassias stability of BVP‐FDEs. Furthermore, some concrete examples to consolidate the obtained results are also considered.
Topics & Concepts
MathematicsFixed-point theoremFractional calculusUniquenessBoundary value problemStability (learning theory)Mathematical analysisBanach fixed-point theoremBanach spaceOrder (exchange)Applied mathematicsDerivative (finance)Function (biology)EconomicsComputer scienceFinanceBiologyFinancial economicsEvolutionary biologyMachine learningFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results