A discretization of the Hadamard fractional derivative

TL;DR

This paper introduces a new discretization method for the Hadamard fractional derivative that simplifies calculations and is applied to solve related differential and variational problems.

Contribution

The paper proposes a novel discretization approach for the Hadamard fractional derivative, enhancing computational efficiency for fractional differential equations.

Findings

Simplified computation of Hadamard fractional derivatives

Effective solution of fractional differential equations

Application to fractional variational problems

Abstract

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.