On fractal space-time and fractional calculus

On fractal space-time and fractional calculus

This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fo...

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Bibliographic Details
Main Authors: Hu Yue, He Ji-Huan
Format: Article
Language:English
Published: VINCA Institute of Nuclear Sciences 2016-01-01
Series:Thermal Science
Subjects:
He's fractional derivative
Adomian's decomposition method
variational iteration method
exp-function method
fractional complex transform
fractional Fornberg-Whitham equation
Online Access:http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-98361603773H.pdf
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spelling doaj-4cee2cb34af04068bfb410f5dc74362f2021-01-02T05:30:08ZengVINCA Institute of Nuclear SciencesThermal Science0354-98362334-71632016-01-0120377377710.2298/TSCI1603773H0354-98361603773HOn fractal space-time and fractional calculusHu Yue0He Ji-Huan1Henan Polytechnic University, School of Mathematics and Information Science, Jiaozuo, ChinaSoochow University, College of Textile and Clothing Engineering, National Engineering Laboratory for Modern Silk, Suzhou, ChinaThis paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-98361603773H.pdfHe's fractional derivativeAdomian's decomposition methodvariational iteration methodexp-function methodfractional complex transformfractional Fornberg-Whitham equation
collection DOAJ
language English
format Article
sources DOAJ
author Hu Yue
He Ji-Huan
spellingShingle Hu Yue
He Ji-Huan
On fractal space-time and fractional calculus
Thermal Science
He's fractional derivative
Adomian's decomposition method
variational iteration method
exp-function method
fractional complex transform
fractional Fornberg-Whitham equation
author_facet Hu Yue
He Ji-Huan
author_sort Hu Yue
title On fractal space-time and fractional calculus
title_short On fractal space-time and fractional calculus
title_full On fractal space-time and fractional calculus
title_fullStr On fractal space-time and fractional calculus
title_full_unstemmed On fractal space-time and fractional calculus
title_sort on fractal space-time and fractional calculus
publisher VINCA Institute of Nuclear Sciences
series Thermal Science
issn 0354-9836
2334-7163
publishDate 2016-01-01
description This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
topic He's fractional derivative
Adomian's decomposition method
variational iteration method
exp-function method
fractional complex transform
fractional Fornberg-Whitham equation
url http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-98361603773H.pdf
work_keys_str_mv AT huyue onfractalspacetimeandfractionalcalculus
AT hejihuan onfractalspacetimeandfractionalcalculus
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