New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM

In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed.