In this paper, we have introduced a fractional-ordered predator-prey population model which has been successfully solved with the help of two powerful analytical methods, namely, Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The fractional derivatives are described in the Caputo sense. Using initial values, we have derived the explicit solutions of predator-prey pop...

and Applied Analysis3[6] J.-H. He, “Variational iteration method—a kind of non-linearanalytical technique: some examples,” International Journal ofNon-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999.[7] J.-H. He, “Variational iteration method-Some recent resultsand new interpretations,” Journal of Computational and AppliedMathematics, vol. 207, no. 1, pp. 3–17, 2...

In this study, two numerical methods—the variational iteration transform method (VITM) and the Adomian decomposition (ADM) method—were used to solve second- fourth-order fractional Boussinesq equations. Both methods are helpful in approximating non-linear problems effectively, easily, accurately. The Atangana–Baleanu operator ZZ were utilized derive solutions for equation. Two examples discusse...

This work aims at a new semi-analytical method called the variational iteration transformation for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu iterative technique are applied to solve suggested problems. proposed has an advantage over existing approaches because it does not require additional materials or computations. Four problems used t...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

The objective of this paper is to present the hybrid variational iteration method. The proposed algorithm is based on the combination of variational iteration and shooting methods. In the proposed algorithm the entire domain is divided into subintervals to establish the accuracy and convergence of the approximate solution. It is found that in each subinterval a three term approximate solution u...

In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.