On a System of ψ-Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions
Muath Awadalla, Kinda Abuasbeh, Muthaiah Subramanian, Murugesan Manigandan
Abstract
In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of ψ-Caputo hybrid fractional derivatives of order 1<υ≤2 subjected to Dirichlet boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of the Leray–Schauder alternative theorem and Banach’s contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam–Hyers. Finally, we provide one example in order to show the validity of our results.
Topics & Concepts
MathematicsUniquenessContraction principleDirichlet boundary conditionBoundary value problemDirichlet distributionOrder (exchange)Mathematical analysisStability (learning theory)Applied mathematicsContraction mappingFixed-point theoremComputer scienceMachine learningFinanceEconomicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems