Local existence and uniqueness of solutions for fractional differential problem with Hilfer-Hadamard fractional derivative

TL;DR

This paper establishes local existence and uniqueness of solutions for fractional differential equations involving Hilfer-Hadamard derivatives, using Picard's iterative method under generalized conditions.

Contribution

It introduces a generalized iterative scheme for solving such equations, relaxing previous restrictive conditions on the nonlinear function.

Findings

Proves local existence and uniqueness of solutions.

Constructs an iterative approximation scheme.

Generalizes conditions on nonlinear functions.

Abstract

This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions imposed on nonlinear function, the iterative scheme for uniformly approximating the solution is constructed.