Applying cuckoo search algorithm to solve fractional differential equation based on cubic spline function

In this paper, a swarm intelligence technique is presented for solving the fractional differential equations (FDE) based on the cubic spline function and cuckoo search algorithm. In this technique, we approximate FDE with the cubic spline approximation and use the cuckoo search algorithm as a tool for the accurate and rapid solution. Based on this method, the given problem is transformed into a problem for solving a nonlinear equation system, and by solving this system, we obtain the solution of FDE. Furthermore, special attention is given to the error analysis of this method. The presented scheme is evaluated on two initial value problems of FDE. The numerical simulation results demonstrate that the proposed algorithm has higher accuracy and is feasible and effective in solving initial value problem of FDE.