Hilfer-Katugampola fractional derivative

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.

21 pages

References in corpus (2)

• New fractional integral unifying six existing fractional integrals
• Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations

Cited by in corpus (2)

• Existence and Stability of Fractional Differential Equations Involving Generalized Katugampola Derivative
• Non-existence of Global Solutions for a Generalized Fractional Differential Problem