Nonlocal Initial Value Problem for Hybrid Generalized Hilfer-type Fractional Implicit Differential Equations
Abdelkrim Salım, Mouffak Benchohra, Jamal Eddine Lazreg, Juan J. Nieto, Yong Zhou
Abstract
Abstract In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.
Topics & Concepts
MathematicsFixed-point theoremFractional calculusNonlinear systemClass (philosophy)Type (biology)Banach spaceMathematical analysisInitial value problemApplied mathematicsValue (mathematics)Fixed pointPure mathematicsPhysicsStatisticsComputer scienceEcologyQuantum mechanicsBiologyArtificial intelligenceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems