Abstract
In this work, a radial basis function (RBF)-based numerical scheme is developed which uses the Coimbra variable time fractional derivative of order $$0<\alpha (t,x)< 1$$ . The Coimbra derivative can efficiently model a dynamical system whose fractional-order behavior changes with time and space locations. The RBF can effectively approximate spatial derivatives in multi-dimensions. The resulted numerical scheme is RBF–FD type and is validated for solute transport problems in 1D and 2D dimension domains. Various cases of variable-order $$0<\alpha (t,x)< 1$$ have been discussed. The present numerical scheme can effectively approximate those variable-order models whose exact solution can not be obtained in a simple way.
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