A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation

Mohammad Hossein Heydari, Zakieh Avazzadeh and Malih Farzi Haromi

Applied Mathematics and Computation, 2019, vol. 341, issue C, 215-228

Abstract: We firstly generalize a multi-term time fractional diffusion-wave equation to the multi-term variable-order time fractional diffusion-wave equation (M-V-TFD-E) by the concept of variable-order fractional derivatives. Then we implement the Chebyshev wavelets (CWs) through the operational matrix method to approximate its solution in the unit square. In fact, we apply the operational matrix of variable-order fractional derivative (OMV-FD) of the CWs to derive the unknown solution. We proceed with coupling the collocation and tau methods to reduce M-V-TFD-E to a system of algebraic equations. The important privilege of method is handling different kinds of conditions, i.e., initial-boundary conditions and Dirichlet boundary conditions, by implementing the same techniques. The convergence and error estimation of the CWs expansion in two dimensions are theoretically investigated. We also examine the applicability and computational efficiency of the new scheme through the numerical experiments.

Keywords: Multi-term variable-order time fractional diffusion-wave equation (M-V-TFD-E); Chebyshev wavelets (CWs); Operational matrix of variable-order Fractional derivative (OMV-FD); Collocation method; Tau method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:341:y:2019:i:c:p:215-228

DOI: 10.1016/j.amc.2018.08.034

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