A computational approach with residual error analysis for the fractional-order biological population model

In this study, a fractional Bernstein series solution method has been submitted to solve the fractional-order biological population model with one carrying capacity. The numerical method has been implemented by an effective algorithm written on the computer algebraic system Maple 15. An error-bound analysis is performed by using a process similar to the RK45 method. An error estimation technique relating to residual function is presented. In the numerical application, the variations in the population of prey and predator with respect to time and situations of these two species relative to each other are plotted. The outputs obtained from our method are compared with the homotopy perturbation Sumudu transform method and reproducing kernel Hilbert space method. The approximate solutions gained from the Bernstein series method are consistent with those of other methods. The advantage of our method is that it requires less computational cost compared with methods involving more complex operations.