Hilfer–Katugampola fractional derivatives

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...

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Bibliographic Details
Published in:Computational & applied mathematics 2018-07, Vol.37 (3), p.3672-3690
Main Authors: Oliveira, D. S., de Oliveira, E. Capelas
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Boundary value problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Derivatives
Differential equations
Integrals
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Volterra integral equations
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Summary: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.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-017-0536-8