Collocation method for solving fractional reaction-diffusion problem arising in chemistry.

In this study, a numerical approach was developed to approximate the solution of the Caputo-type fractional reaction-diffusion problem. In the proposed method, the Caputo fractional derivative and the integer derivatives of the equation are obtained using the operational matrices of the collocation method with orthogonalized Bernoulli polynomial bases. This method reduces the main problem to a system of algebraic equations. On the other hand, by solving this system, an approximation for the desired equation is obtained. The main feature of the presented method is the sparse of the operational matrices, which reduces the computational cost. The convergence analysis and error bounds to establish the validity of the developed method are discussed. This method is tested by six numerical problems to demonstrate the capability of the suggested new technique. Also, the obtained results are compared with the existing methods in the literature. The results indicate that the proposed method is an efficient and reliable approach for solving the problem.