Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets
Applied and Computational Mathematics
Volume 5, Issue 4, August 2016, Pages: 177-185
Received: Aug. 6, 2016;
Accepted: Aug. 15, 2016;
Published: Sep. 2, 2016
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I. K. Youssef, Department of Mathematics, Ain Shams University, Cairo, Egypt
A. R. A. Ali, Department of Mathematics, Baghdad University, Baghdad, Iraq
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.
I. K. Youssef,
A. R. A. Ali,
Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets, Applied and Computational Mathematics.
Vol. 5, No. 4,
2016, pp. 177-185.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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