Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets

I. K. Youssef; A. R. A. Ali

doi:doi:10.11648/j.acm.20160504.12

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Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets

I. K. Youssef, A. R. A. Ali

Published in Applied and Computational Mathematics (Volume 5, Issue 4)

Received: 6 August 2016 Accepted: 15 August 2016 Published: 2 September 2016

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Abstract

Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.

Published in	Applied and Computational Mathematics (Volume 5, Issue 4)
DOI	10.11648/j.acm.20160504.12
Page(s)	177-185
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Haar Wavelet, Operational Matrix, Fractional Derivative, Diffusion Like Equation

References

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[4]	I. K. Youssef, A. M. Shukur, The line method combined with spectral chebyshev for space-time fractional diffusion equation, Applied and Computational Mathematics 3 (6) (2014) 330-336.
[5]	I. K. Youssef, A. M. Shukur, Modified variation iteration method for fraction space-time partial differential heat and wave equations, International Journal 2 (2) (2013) 1000–1013.
[6]	I. K. Youssef, A. R. A. Ali, Memory Effects in Diffusion Like Equation Via Haar Wavelets, Pure and Applied Mathematics Journal, 5 (4), (2016) 130-140.
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APA Style

I. K. Youssef, A. R. A. Ali. (2016). Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets. Applied and Computational Mathematics, 5(4), 177-185. https://doi.org/10.11648/j.acm.20160504.12

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ACS Style

I. K. Youssef; A. R. A. Ali. Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets. Appl. Comput. Math. 2016, 5(4), 177-185. doi: 10.11648/j.acm.20160504.12

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AMA Style

I. K. Youssef, A. R. A. Ali. Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets. Appl Comput Math. 2016;5(4):177-185. doi: 10.11648/j.acm.20160504.12

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@article{10.11648/j.acm.20160504.12,
  author = {I. K. Youssef and A. R. A. Ali},
  title = {Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {4},
  pages = {177-185},
  doi = {10.11648/j.acm.20160504.12},
  url = {https://doi.org/10.11648/j.acm.20160504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160504.12},
  abstract = {Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.},
 year = {2016}
}

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TY  - JOUR
T1  - Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets
AU  - I. K. Youssef
AU  - A. R. A. Ali
Y1  - 2016/09/02
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DO  - 10.11648/j.acm.20160504.12
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PB  - Science Publishing Group
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AB  - Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.
VL  - 5
IS  - 4
ER  -

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Author Information

I. K. Youssef

Department of Mathematics, Ain Shams University, Cairo, Egypt
A. R. A. Ali

Department of Mathematics, Baghdad University, Baghdad, Iraq

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APA Style

I. K. Youssef, A. R. A. Ali. (2016). Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets. Applied and Computational Mathematics, 5(4), 177-185. https://doi.org/10.11648/j.acm.20160504.12

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ACS Style

I. K. Youssef; A. R. A. Ali. Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets. Appl. Comput. Math. 2016, 5(4), 177-185. doi: 10.11648/j.acm.20160504.12

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AMA Style

I. K. Youssef, A. R. A. Ali. Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets. Appl Comput Math. 2016;5(4):177-185. doi: 10.11648/j.acm.20160504.12

Copy | Download

@article{10.11648/j.acm.20160504.12,
  author = {I. K. Youssef and A. R. A. Ali},
  title = {Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {4},
  pages = {177-185},
  doi = {10.11648/j.acm.20160504.12},
  url = {https://doi.org/10.11648/j.acm.20160504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160504.12},
  abstract = {Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets
AU  - I. K. Youssef
AU  - A. R. A. Ali
Y1  - 2016/09/02
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160504.12
DO  - 10.11648/j.acm.20160504.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 177
EP  - 185
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160504.12
AB  - Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.
VL  - 5
IS  - 4
ER  -

Copy | Download