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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. [ABSTRACT FROM AUTHOR]

The present work aims to approximate the solution of linear time fractional PDE with Caputo Fabrizio derivative. For the said purpose Laplace transform with local radial basis functions is used. The Laplace transform is applied to obtain the corresponding time independent equation in Laplace space and then the local RBFs are employed for spatial discretization. The solution is then represented as a contour integral in the complex space, which is approximated by trapezoidal rule with high accuracy. The application of Laplace transform avoids the time stepping procedure which commonly encounters the time instability issues. The convergence of the method is discussed also we have derived the bounds for the stability constant of the differentiation matrix of our proposed numerical scheme. The efficiency of the method is demonstrated with the help of numerical examples. For our numerical experiments we have selected three different domains, in the first test case the square domain is selected, for the second test the circular domain is considered, while for third case the L-shape domain is selected.