In this paper, we construct an analytical study of the epidemic pine wilt disease model in a Caputo-Fabrizio type fractional order; the basic properties of the fractional differential equation and the model are presented; we give the basic properties of the model. Applying the homotopy analysis transform method to obtain numerical solutions to the model, the numerical result represented in graphs is presented.

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In this paper, we construct an analytical solution of the coupled Burgers’ equation, using the homotopy analysis method, which is a semi-analytical method, the approximate solution obtained by this method is convergent for different values of the convergence control parameter ℏ, the optimal value of ℏ corresponding with the minimum error to be determined by the residual. The results obtained by the present method are compared with other obtained solutions by different numerical methods.