Abstract
Fractional differential equations depict nature sufficiently in light of the symmetry properties which describe biological and physical processes. This article is concerned with the numerical treatment of three-term time fractional-order multi-dimensional diffusion equations by using an efficient local meshless method. The space derivative of the models is discretized by the proposed meshless procedure based on the multiquadric radial basis function though the time-fractional part is discretized by Liouville–Caputo fractional derivative. The numerical results are obtained for one-, two- and three-dimensional cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.
Highlights
Over the most recent couple of decades, fractional-order differential equations have been effectively utilized for modeling a wide range of processes and systems in the applied sciences and engineering
The local meshless method (LMM) [26,31] is utilized for the solution of time-fractional convection-diffusion models
This section is concerned with the numerical results of the one, two- and three-dimensional three-term time-fraction diffusion model equations utilizing the suggested efficient local meshless method (LMM)
Summary
Over the most recent couple of decades, fractional-order differential equations have been effectively utilized for modeling a wide range of processes and systems in the applied sciences and engineering. The basic information on fractional calculus can be found in [1,2,3]. The extensive applications in science and engineering are portrayed by fractional partial differential equation (PDEs) [4,5,6,7,8]. It is observed that the multi-term time-fractional PDEs are suggested to improve the modelling accuracy in depicting the anomalous diffusion process, modeling different sorts of viscoelastic damping, precisely catching power-law frequency dependence and simulating flow of a fractional Maxwell fluid [9]. Numerous methods have been employed for the solution like finite difference method [10], homotopy analysis method [11,12], meshless method [13,14,15,16], Riccati transformation approach [17], Adomian decomposition method [18], expansion methods [19,20]
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