Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations
Ashwini D. Mali, Kishor D. Kucche
Abstract
In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving Ψ‐Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam–Hyers, and Ulam–Hyers–Rassias stability have been acquired by means of an equivalent fractional integral equation. Our investigations depend on the fixed‐point theorem due to Krasnoselskii and the Gronwall inequality involving Ψ‐Riemann–Liouville fractional integral. Finally, examples are provided to show the utilization of primary outcomes.
Topics & Concepts
MathematicsFractional calculusGronwall's inequalityFixed-point theoremMathematical analysisBoundary value problemIntegral equationStability (learning theory)Applied mathematicsInequalityMachine learningComputer scienceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems