A computational method for solving variable-order fractional nonlinear diffusion-wave equation

Mohammad Hossein Heydari, Zakieh Avazzadeh and Yin Yang

Applied Mathematics and Computation, 2019, vol. 352, issue C, 235-248

Abstract: In this paper, we generalize a one-dimensional fractional diffusion-wave equation to a one-dimensional variable-order space-time fractional nonlinear diffusion-wave equation (V-OS-TFND-WE) where the variable-order fractional derivatives are considered in the Caputo type. To solve this introduced equation, an easy-to-follow method is proposed which is based on the Chebyshev cardinal functions coupling with the tau and collocation methods. To carry out the method, an operational matrix of variable-order fractional derivative (OMV-OFD) is derived for the Chebyshev cardinal functions to be employed for expanding the unknown function. The proposed method can provide highly accurate approximate solutions by reducing the problem under study to a system of nonlinear algebraic equations which is technically simpler for handling. The experimental results confirm the applicability and effectiveness of the method.

Keywords: Variable-order space-time fractional nonlinear diffusion-wave equation (V-OS-TFND-WE); Chebyshev cardinal functions; Operational matrix of variable-order fractional derivative (OMV-OFD); Tau-collocation method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:352:y:2019:i:c:p:235-248

DOI: 10.1016/j.amc.2019.01.075

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