Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives
Abdulkafi Mohammed Saeed, Mohammed S. Abdo, Mdi Begum Jeelani
Abstract
In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.
Topics & Concepts
UniquenessMathematicsStability (learning theory)Fixed-point theoremFrame (networking)Order (exchange)Class (philosophy)Banach spaceFixed pointApplied mathematicsFractional calculusFunction (biology)Pure mathematicsMathematical analysisComputer scienceEvolutionary biologyMachine learningEconomicsBiologyTelecommunicationsArtificial intelligenceFinanceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems