In this paper, we present a numerical method to approximate the solution of the multi-term time fractional diffusion-wave equation (M-TFDWE). The proposed method represents the solution as a sum of shifted Gegenbauer polynomials (SGPs) with unknown coefficients. By using the operational matrix of fractional integration and integer derivatives based on SGPs, the M-TFDWE is converted into a system of algebraic equations. The convergence analysis of this numerical method is also discussed. Finally, we provide two examples to illustrate the accuracy of the proposed method.
Molavi-Arabshahi, M. , Rashidinia, J. and Tanoomand, S. (2025). Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method. Computational Methods for Differential Equations, 13(3), 815-827. doi: 10.22034/cmde.2024.61509.2660
MLA
Molavi-Arabshahi, M. , , Rashidinia, J. , and Tanoomand, S. . "Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method", Computational Methods for Differential Equations, 13, 3, 2025, 815-827. doi: 10.22034/cmde.2024.61509.2660
HARVARD
Molavi-Arabshahi, M., Rashidinia, J., Tanoomand, S. (2025). 'Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method', Computational Methods for Differential Equations, 13(3), pp. 815-827. doi: 10.22034/cmde.2024.61509.2660
CHICAGO
M. Molavi-Arabshahi , J. Rashidinia and S. Tanoomand, "Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method," Computational Methods for Differential Equations, 13 3 (2025): 815-827, doi: 10.22034/cmde.2024.61509.2660
VANCOUVER
Molavi-Arabshahi, M., Rashidinia, J., Tanoomand, S. Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method. Computational Methods for Differential Equations, 2025; 13(3): 815-827. doi: 10.22034/cmde.2024.61509.2660
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