A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces
Abdelatif Boutiara, Sina Etemad, Sabri T. M. Thabet, Sotiris K. Ntouyas, Shahram Rezapour, Jessada Tariboon
Abstract
In this paper, we study a coupled fully hybrid system of (k,Φ)–Hilfer fractional differential equations equipped with non-symmetric (k,Φ)–Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (GBS). Moreover, the Ulam–Hyers (UH) stability of the solutions is discussed by using the Urs’s method. Finally, an illustrated example is given to confirm the validity of our results.
Topics & Concepts
MathematicsUniquenessBanach spaceFixed-point theoremApplied mathematicsStability (learning theory)Order (exchange)Context (archaeology)Fractional calculusPure mathematicsMatrix (chemical analysis)Mathematical analysisComputer scienceEconomicsBiologyMachine learningComposite materialFinancePaleontologyMaterials scienceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems