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arXiv · 1705.07733

Hilfer-Katugampola fractional derivative

D. S. Oliveira·E. Capelas de Oliveira
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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.

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D. S. Oliveira, E. Capelas de Oliveira. 2017-11-10. Hilfer-Katugampola fractional derivative. https://arxiv.org/abs/1705.07733

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