Abstract
In this paper, we present a high order new numerical approximation for variable order Caputo fractional derivative of order 0<α(x,t)<1, by using the idea of interpolation. Then, by using this approximation, a numerical scheme is presented by using finite difference approach for variable order time fractional reaction-subdiffusion equation (VO-TFRSDE). The unconditionally stability of the numerical scheme is examined theoretically. The scheme is implemented on the two test problems. The numerical results are highly accurate with higher order of convergence.
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