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In this article, we present a new second order finite difference discretescheme for fractal mobile/immobile transport model based on equivalenttransformative Caputo formulation. The new transformative formulation takes thesingular kernel away to make the integral calculation more efficient.Furthermore, this definition is also effective where $\alpha$ is a positiveinteger. Besides, the T-Caputo derivative also helps to increase theconvergence rate of the discretization of $\alpha$-order($0<\alpha<1$) Caputoderivative from $O(\tau^{2-\alpha})$ to $O(\tau^{3-\alpha})$, where $\tau$ isthe time step. For numerical analysis, a Crank-Nicholson finite differencescheme to solve fractal mobile/immobile transport model is introduced andanalyzed. The unconditional stability and a priori estimates of the scheme aregiven rigorously. Moreover, the applicability and accuracy of the scheme aredemonstrated by numerical experiments to support our theoretical analysis.

journal of mathematical physics

A novel second order finite difference discrete scheme for fractal  mobile/immobile transport model based on equivalent transformative Caputo  formulation