Numerical methods for solving the multi-term time-fractional wave-diffusion equation
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Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations and can be extended to other kinds of themulti-term fractional time-space models with fractional Laplacian.Abstract:
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.read more
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Computational Study of Multiterm Time-Fractional Differential Equation Using Cubic B-Spline Finite Element Method
TL;DR: In this article , a numerical method based on cubic B-spline finite element method for the solution of multiterm time-fractional differential equations is presented, where the temporal fractional part is defined in the Caputo sense while the Bspline method is employed for space approximation, and the stability of the proposed scheme is discussed by the Von Neumann method.
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TL;DR: In this article , a class of time-fractional diffusion and sub-diffusion equations were solved by constructing two-dimensional Genocchi-frractional Laguerre functions (G-FLFs) using pseudo-operational matrices.
References
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