Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations

Abstract

The Cauchy-type problem for a nonlinear differential equation involving Hilfer fractional derivative is considered. We prove existence, uniqueness and continuous dependence of a solution for Cauchy-type problem using successive approximations and generalized Gronwall inequality.

Cited by in corpus (6)

• Hilfer-Katugampola fractional derivative
• On existence and approximation of solution of nonlinear Hilfer fractional differential equation
• On Ulam type stability for nonlinear implicit fractional differential equations
• Local existence and uniqueness of solutions for fractional differential problem with Hilfer-Hadamard fractional derivative
• Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem
• Non-existence of Global Solutions for a Generalized Fractional Differential Problem