Qualitative Study on Solutions of Piecewise Nonlocal Implicit Fractional Differential Equations
Mohammed S. Abdo, Sahar Ahmed Idris, Wedad Albalawi, Abdel‐Haleem Abdel‐Aty, Mohammed Zakarya, Emad E. Mahmoud
Abstract
In this paper, we investigate new types of nonlocal implicit problems involving piecewise Caputo fractional operators. The existence and uniqueness results are proved by using some fixed point theorems. Furthermore, we present analogous results involving piecewise Caputo-Fabrizio and Atangana–Baleanu fractional operators. The ensuring of the existence of solutions is shown by Ulam-Hyer’s stability. At last, two examples are given to show and approve our outcomes.
Topics & Concepts
UniquenessMathematicsPiecewiseStability (learning theory)Fixed-point theoremFractional calculusApplied mathematicsFixed pointOperator (biology)Mathematical analysisCalculus (dental)Computer scienceGeneBiochemistryMedicineRepressorTranscription factorChemistryMachine learningDentistryFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems