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

H. M. Srivastava, Khaled M. Saad, Eman H. F. Al-Sharif

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.


Keywords


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

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v10i4.961

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