Hilfer-Katugampola fractional derivative

2017/05/15 by D. S. Oliveira, Oliveira, D. S., E. Capelas de Oliveira +1
Engineering · Mathematics · #26A33 #Advanced Control Systems Design #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1705.07733

openalex publication_date 2017/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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