Abstract
A transform based local RBF method for 2D linear PDE with Caputo–Fabrizio derivative
Highlights
Fractional calculus is the branch of mathematics in which the differential or integral operators with arbitrary orders are studied
In literature a lot of valuable work is available in which the authors have studied various fractional derivatives and their applications
The investigation of numerous phenomena like electrodynamics, elasticity, diffusion process, fluid flow, signal and image processing, hydrology and many others can be done with the help of fractional PDEs [4, 17]
Summary
Fractional calculus is the branch of mathematics in which the differential or integral operators with arbitrary orders are studied. The researchers have developed various methods for modeling the numerical and the analytical solutions of time-fractional order PDEs with CF derivative. In [17] the authors have solved linear PDEs with CF derivative using Laplace homotopy analysis method. In [5] the author’s studied numerical approximation of space-time CF fractional derivative and its application to groundwater pollution equation via Crank–Nicholson scheme. In [16] the authors have obtained the fundamental solution of advection-diffusion problem with CF derivative using Laplace and Fourier transforms. In this article we propose a numerical scheme which is based on the Laplace transform(LT) and local radial basis functions (RBFs) for the approximation of the solution of linear time fractional PDEs with CF derivative over complex domians. The advantage of using the Laplace transformation is the less computational cost and no time instability issue
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