Welcome to the InfoSci Platform
On the Approximate Solution of Caputo-Riesz-Feller Fractional Diffusion Equation

On the Approximate Solution of Caputo-Riesz-Feller Fractional Diffusion Equation

Samir Shamseldeen, Ahmed Elsaid, Seham Madkour
Copyright: © 2020 |Pages: 21
ISBN13: 9781799831228|ISBN10: 1799831221|ISBN13 Softcover: 9781799831235|EISBN13: 9781799831242
DOI: 10.4018/978-1-7998-3122-8.ch010
Cite Chapter Cite Chapter

MLA

Shamseldeen, Samir, et al. "On the Approximate Solution of Caputo-Riesz-Feller Fractional Diffusion Equation." Advanced Applications of Fractional Differential Operators to Science and Technology, edited by Ahmed Ezzat Matouk, IGI Global, 2020, pp. 224-244. https://doi.org/10.4018/978-1-7998-3122-8.ch010

APA

Shamseldeen, S., Elsaid, A., & Madkour, S. (2020). On the Approximate Solution of Caputo-Riesz-Feller Fractional Diffusion Equation. In A. Matouk (Ed.), Advanced Applications of Fractional Differential Operators to Science and Technology (pp. 224-244). IGI Global. https://doi.org/10.4018/978-1-7998-3122-8.ch010

Chicago

Shamseldeen, Samir, Ahmed Elsaid, and Seham Madkour. "On the Approximate Solution of Caputo-Riesz-Feller Fractional Diffusion Equation." In Advanced Applications of Fractional Differential Operators to Science and Technology, edited by Ahmed Ezzat Matouk, 224-244. Hershey, PA: IGI Global, 2020. https://doi.org/10.4018/978-1-7998-3122-8.ch010

Export Reference

Mendeley
Favorite

Abstract

In this work, a space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative is introduced. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. Also, a very useful Riesz-Feller fractional derivative is proved; the property is essential in applying iterative methods specially for complex exponential and/or real trigonometric functions. The analytic series solution of the problem is obtained via the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to highlight the effect of changing the fractional derivative parameters on the behavior of the obtained solutions. The results in this work are originally extracted from the author's work.

Request Access

You do not own this content. Please login to recommend this title to your institution's librarian or purchase it from the IGI Global bookstore.