Hilfer-Katugampola fractional derivative
Classical Analysis and ODEs
2017-11-13 v2 Mathematical Physics
math.MP
Abstract
We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type. As an application, we consider a nonlinear fractional differential equation with an initial condition using this new formulation. We show that this equation is equivalent to a Volterra integral equation and demonstrate the existence and uniqueness of solution to the nonlinear initial value problem.
Cite
@article{arxiv.1705.07733,
title = {Hilfer-Katugampola fractional derivative},
author = {D. S. Oliveira and E. Capelas de Oliveira},
journal= {arXiv preprint arXiv:1705.07733},
year = {2017}
}
Comments
21 pages