A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model

摘要: Evolution equations containing fractional derivatives can provide suitable mathematical models for describing anomalous diffusion and transport dynamics in complex systems that cannot be modeled accurately by normal integer order equations. Recently, researchers have found many physical processes exhibit behavior varies with time or space. The continuum of the calculus allows operator to considered as a variable. In this paper, we consider mobile-immobile advection-dispersion model Coimbra variable derivative which is preferable modeling dynamical more efficient from numerical standpoint. A novel implicit method equation proposed stability approximation investigated. As convergence method, only special case, i.e., independent t. case where depends on both t space x will future work. Finally, examples are provided show difference computationally efficient.