Caputo-Hadamard fractional derivatives of variable order
Provides new mathematical definitions and approximation methods for variable-order fractional calculus, relevant to mathematicians and applied scientists working with fractional models.
The paper introduces three types of Caputo-Hadamard fractional derivatives with variable order, derives integer-order approximations with error estimates, and validates them on a concrete example.
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.