Caputo-Hadamard fractional derivatives of variable order

Abstract

In this paper we present three types of Caputo-Hadamard derivatives of variable fractional order, and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained, and an estimation for the error is given. At the end we compare the exact fractional derivative of a concrete example with some numerical approximations.

This is a preprint of a paper whose final and definite form will appear in Numerical Functional Analysis and Optimization