Subdivision-based collocation methods for time fractional convection diffusion reaction equation with environmental and biomedical applications

Time-fractional convection diffusion reaction (TFCDR) equations are useful mathematical models to describe transport processes with memory and anomalous diffusion. Many scientific and engineering problems lead to such models, such as contaminant migration in groundwater, dispersion of atmospheric pollutants, delivery of drugs to patients, transport of biological tissue, reaction of chemicals in a heterogeneous medium. In this paper, a subdivision-based collocation method is constructed and used to numerically solve TFCDR equations. The fractional time derivative is taken in the Caputo sense, which gives the possibility to include meaningful initial conditions. The spatial domain is subdivided into uniform segments and approximated using subdivision basis functions. A fully discrete numerical formulation is developed and the stability and convergence of that formulation is thoroughly investigated. The results show that for various values of the fractional order, convection coefficient, diffusion parameter and reaction rate, the proposed subdivision based collocation result is stable and accurate, and the solution obtained by the proposed approach is accurate and stable with low computational cost. The comparisons with exact solutions and existing numerical techniques confirm the effectiveness and efficiency of the proposed method.