This review is an elementary introduction to the concepts of the recently developed
asymptotic methods and new developments. Particular attention is paid throughout the …

This review features a survey of some recent developments in asymptotic techniques and
new developments, which are valid not only for weakly nonlinear equations, but also for …

In this research, an integro-differential equation which describes the charged particle motion
for certain configurations of oscillating magnetic fields is considered. The homotopy …

Solutions of singular IVPs of Lane–Emden type by homotopy perturbation method -
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Series solutions of the Lane–Emden equation based on either a Volterra integral equation
formulation or the expansion of the dependent variable in the original ordinary differential …

In this study, we present a framework to obtain analytical solutions to nonlinear fractional
Schrödinger equations. The homotopy perturbation method (HPM) is employed to derive …

In this study, the homotopy perturbation method proposed by Ji-Huan He is applied to solve
both linear and nonlinear boundary value problems for fourth-order integro-differential …

In this paper, the He's homotopy perturbation method is applied to solve systems of Volterra
integral equations of the second kind. Some examples are presented to illustrate the ability …

In this paper, we conduct a comparative study among He's homotopy perturbation method
and three traditional methods for an analytic and approximate treatment of nonlinear integral …

In this study, homotopy perturbation method (HPM) is used to obtain analytic and
approximate solutions of the space-and time-fractional telegraph equations. The space-and …