Fractional Ecosystem Model and Its Solution by Homotopy Perturbation Method

In the present paper we propose an algorithm based on Homotopy Perturbation Method to solve the fractional Ecosystem model and show the efficiency and accuracy of the algorithm . This Ecosystem model is solved with time fractional derivatives in the sense of Caputo. The nonlinear terms can be easily handled by the using He’s Polynomials. The numerical solutions of the Ecosystem model reveal that only a few iterations are sufficient to obtained accurate approximate analytical solutions. The numerical results obtained are presented graphically. The four different cases are considered and proved that the method is extremely effective due to fractional approach and performance. Comparing the methodology (FHPM) with the some known technique (HPM) shows that the present approach is effective and powerful. The proposed scheme finds the solution with the help of Mathematica and without any restrictive assumptions. We implement it to four different problems.