Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative

TL;DR

This paper derives series expansion formulas for Hadamard fractional integrals and derivatives, providing error bounds and demonstrating the effectiveness of the approximation through numerical simulations.

Contribution

It introduces new series expansion formulas for Hadamard fractional calculus and analyzes their accuracy and computational efficiency.

Findings

Derived series expansion formulas for Hadamard fractional operators.

Provided error bounds for finite sum approximations.

Numerical simulations confirm the method's efficiency.

Abstract

We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of the approximation method.