Abstract
In this paper, fractional version of advection–diffusion equation (FADE) has been considered for the numerical solution. It is acquired from the classical advection–diffusion equation (ADE) by substituting the space and time derivatives with a generalized Caputo fractional derivative. Moreover, we have proposed novel discretization for space and time using radial basis functions and Chebyshev polynomials, respectively. The proposed scheme is truly meshless thereby able to manage both space and time fractional derivatives simultaneously with appropriate boundary conditions. Lastly, we have discussed numerical example to affirm this proposed scheme whilst revealing the accuracy and performance of the same.
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