Pure and Applied Mathematics Journal
Volume 5, Issue 4, August 2016, Pages: 130-140
Received: Jul. 17, 2016;
Accepted: Jul. 26, 2016;
Published: Aug. 10, 2016
Views 3310 Downloads 99
I. K. Youssef, Department of Mathematics, Ain Shams University, Cairo, Egypt
A. R. A. Ali, Department of Mathematics, Baghdad University, Baghdad, Iraq
The memory and hereditary effects of fractional derivatives as well as integral terms are considered in a diffusion like problem. The Haar wavelet operational matrix technique is employed to solve fractional order diffusion equation with time dependent integral term and time dependent boundary condition. The fractional derivative is described in the Caputo sense. The effect of using inverse fractional operator which combines the memory behaviors of the fractional derivatives to all other terms in the equation is disscused. Different Haar bases functions are used (8, 16, 32, 64) and comparison of the wavelet operational matrix is considered. Error analysis is considered. A general numerical example with four subproblems is considered, graphical representation of the different solutions as well as their errors are given.
I. K. Youssef,
A. R. A. Ali,
Memory Effects in Diffusion Like Equation Via Haar Wavelets, Pure and Applied Mathematics Journal.
Vol. 5, No. 4,
2016, pp. 130-140.
Copyright © 2016 Authors retain the copyright of this article.
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