Numerical simulation of the distributed-order time-fractional mobile–immobile equation by the local radial basis function-compact finite difference method

This paper presents a high-order local meshless technique for simulating the distributed-order time-fractional mobile–immobile equation in two and three-dimensional cases. For this purpose, the time variable is discretized using the finite difference approach, along with a weighted and shifted Grünwald difference (WSGD) approximation. In the semi-discretization process, the distributed-order term is approximated using a numerical integration technique. Afterwards, the stability and convergence of the time semi-discrete scheme are studied via the energy method. The discretization process is completed by applying the meshless radial basis function-compact finite difference (RBF-CFD) technique for spatial discretization. Finally, some numerical experiments are performed on regular and irregular domains to show the efficiency and accuracy of the proposed method.