Nonlocal Boundary Value Problem for Generalized Hilfer Implicit Fractional Differential Equations

Abstract

In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving $\phi$-Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam-Hyers, and Ulam-Hyers-Rassias stability has been acquired by means equivalent fractional integral equation. Our investigations depend on the fixed point theorem due to Krasnoselskii and the Gronwall inequality involving $\phi$-Riemann--Liouville fractional integral. An example is provided to show the utilization of primary outcomes.

arXiv comment24

References in corpus (6)

• Stability of $\psi$-Hilfer Impulsive Fractional Differential Equations
• On the Nonlinear $\Psi$-Hilfer Fractional Differential Equations
• On the existence and stability for non-instantaneuos impulsive fractional integrodifferential equation
• On the Impulsive Implicit $\Psi$--Hilfer Fractional Differential Equations with Delay
• On the Ulam-Hyers stabilities of Ψ-Hilfer fractional differential equation by means of abstract Volterra operator
• A Gronwall inequality and the Cauchy-type problem by means of $\psi$-Hilfer operator

Cited by in corpus (2)

• On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations
• Analysis of Hilfer fractional integro-differential equations with almost sectorial operators