· 2015
A new Definition of Fractional Derivative without Singular Kernel
- 2,441citations
- 2015year
Short summary
Researchers introduce a novel definition for fractional derivatives using a smooth, non-singular kernel, offering distinct representations for temporal and spatial variables.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces a fractional derivative definition with a smooth, non-singular kernel.
- Employs distinct representations for temporal (Laplace transform compatible) and spatial (Fourier transform compatible) variables.
- Aims to model non-local systems with material heterogeneities and multi-scale fluctuations.
- Offers an alternative to classical local theories and singular-kernel fractional models.
AI-generated from the title and abstract; the full text is not read.
Abstract
In the paper, we present a new definition of fractional deriva tive with a smooth kernel which takes on two different representations for the temporal and spatial variable. The first works on the time variables; thus it is suitable to use th e Laplace transform. The second definition is related to the spatial va riables, by a non-local fractional derivative, for which it is more convenient to work with the Fourier transform. The interest for this new approach with a regular kernel was born from the prospect that there is a class of non-local systems, which have the ability to descri be the material heterogeneities and the fluctuations of diff erent scales, which cannot be well described by classical local theories or by fractional models with singular kernel.
The authors' abstract, as published at the source., 2015 · DOI ↗
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Field: Modeling and Simulation
Modeling and SimulationMathematics