In this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial dierential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopyperturbation method in order to reformulate initial value problem. Some illustrative examples aregiven in ord...

in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

In this paper, a Laplace homotopy analysis method which is based on homotopy analysis method and Laplace transform is applied to obtain the approximate solutions of fractional linear and non-linear differential equations. The proposed algorithm presents a procedure of constructing the set of base functions and gives a high-order deformation equation in simple form. Numerical examples are includ...

In this paper, we introduce an efficient method for solving the quadratic Riccati differential equation. In this technique, combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm to the exact solution of the nonlinear Riccati equation. Unlike the previous approach for this problem, so-called NHPM, the present method, does not need the init...

In this study, we present a new general solution to rational epidemiological mathematical model via recent intelligent method called the natural transform homotopy analysis (NTHAM), which combines two methods: (NTM) and (HAM). To assess precision reliability of method, compared obtained results with those Laplace perturbation (LHPM) as well q-homotopy Sumudu (q-HASTM), revealed that NTHAM is mo...