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Numerical methods for solving the multi-term time-fractional wave-diffusion equation

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TLDR
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.

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Citations
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Inverse source problem for a space-time fractional diffusion equation

TL;DR: In this article, an inverse source problem for a space-time fractional diffusion equation is formulated as a minimization problem and an iterative process is developed for identifying the unknown source term.

Meshfree numerical integration for some challenging multi-term fractional order PDEs

TL;DR: In this paper , the mesh-free Radial Basis Function (RBF) was used to solve the time-space fractional PDE problems. But the accuracy of the suggested scheme was analyzed by using the L ∞ norm.
Journal ArticleDOI

Novel numerical techniques for the finite moment log stable computational model for European call option

TL;DR: In this paper, the authors considered the finite difference method to approximate the finite moment log stable (FMLS) model and presented two numerical schemes for this approximation: the implicit numerical scheme and the Crank-Nicolson scheme.
References
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Journal ArticleDOI

The random walk's guide to anomalous diffusion: a fractional dynamics approach

TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI

Analysis of Fractional Differential Equations

TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
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