Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation

The objective of this paper is to find the numerical solution of two-dimensional multi-term time fractional mobile-immobile equation. The proposed technique is based on the arbitrary-order orthogonal spline collocation method for the spatial discretization, the L1 approximation for the Caputo fractional derivative, and a second-order backward differentiation formula in time. The stability and convergence are proved in detail. Then, the convergence analysis is validated by a number of numerical experiments.