Hilfer–Katugampola fractional derivatives

Journal Article · Sun Jul 15 00:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0536-8· OSTI ID:22769265

Oliveira, E. Capelas de, ^[1]

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1. Imecc-Unicamp, Department of Applied Mathematics (Brazil)

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.

• OSTI ID: 22769265
• Journal Information: Computational and Applied Mathematics, Vol. 37, Issue 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
DIFFERENTIAL EQUATIONS
INTEGRALS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
VOLTERRA INTEGRAL EQUATIONS