A New Analysis of the Time-Fractional and Space-Time Fractional-Order Nagumo Equation

Authors

  • H. M. Srivastava Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
  • Khaled M. Saad Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Kingdom of Saudi Arabia; Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen
  • Eman H. F. Al-Sharif Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Kingdom of Saudi Arabia

DOI:

https://doi.org/10.26713/jims.v10i4.961

Keywords:

Adomian Decomposition Method (ADM), Time-fractional Nagumo equation, Space-time fractional-order Nagumo equation, Convergence analysis

Abstract

In this paper, we present an algorithm by using the Adomian Decomposition Method (ADM) in order to solve the time-fractional Nagumo equation and the space-time fractional-order Nagumo equation. In the space-time fractional case, we expand the \(tanh(\cdot)\) initial condition in the basis functions \(e^{−n\zeta}\). The fractional-order derivative could then be easily calculated. An important point in our investigation is that many earlier authors avoided this initial condition as there was no direct method to calculate its fractional derivative. We have studied the convergence analysis and applied it to the time-fractional Nagumo equation and the space-time fractional-order Nagumo equation. We compare the ADM solution with the exact solution and find a very good agreement. We also graphically illustrate the behavior of the ADM solutions.

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Published

2018-12-31
CITATION

How to Cite

Srivastava, H. M., Saad, K. M., & Al-Sharif, E. H. F. (2018). A New Analysis of the Time-Fractional and Space-Time Fractional-Order Nagumo Equation. Journal of Informatics and Mathematical Sciences, 10(4), 545–561. https://doi.org/10.26713/jims.v10i4.961

Issue

Vol. 10 No. 4 (2018)

Section

Research Articles

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