Finite difference/collocation method to solve multi term variable-order fractional reaction–advection–diffusion equation in heterogeneous medium

Abstract

Fractional order models are more complicated to solve in comparison to the integer-order model. When it comes to variable order models the complexity of the model even further increases. In the present article, the authors developed an efficient method with the help of Fibonacci collocation and finite difference method to solve the multi-term variable-order fractional reaction–advection–diffusion model in the heterogeneous medium. The authors used the discussed method to solve a multi-term variable-order fractional diffusion model having an exact solution and compared the numerical results obtained from the discussed and previously solved methods to show that the proposed method works better than the previously solving method. After validation of the accuracy of the method, the authors have used it to solve the considered model. The effects on the diffusion process due to changes in various parameters of the model in the heterogeneous medium are shown graphically. © 2020 Wiley Periodicals LLC