Integrated Lucas and Fibonacci polynomial approach for time fractional fast and slow diffusion models

This paper presents the numerical method utilized for approximate solution of fast and slow diffusion models having fractional order derivative in time. The proposed method approximates the time derivative of the model using L1-formula and applies the integrated Lucas and Fibonacci polynomial functions for approximating the unknown functions and their derivatives. Then, with the help of spatial discretization, the approximated model is converted into system of linear equations. The performance of the proposed algorithm was studied by calculating the solutions of one- and two-dimensional fast and slow diffusion models and these solutions were compared with the existing methods. The comparison illustrates that the proposed method is robust and highly efficient.