In this paper, we present new ideas for the implementation of homotopy asymptotic method
(HAM) to solve systems of nonlinear fractional differential equations (FDEs). An effective …

A ratio approach based on the simple ratio test associated with the terms of homotopy series
was proposed by the author in the previous publications. It was shown in the latter through …

In this study, an optimal homotopy analysis approach will be described to deal with
nonlinear fractional differential equations. The proposed approach presents a procedure to …

This paper studies a parameter estimation problem for the non-linear diffusion equation
within multiphase porous media flow, which has important applications in the field of oil …

In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear
reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs …

This paper presents an improved optimal homotopy analysis algorithm to deal with
nonlinear first-order differential equations. We discuss the optimal selection of the auxiliary …

The models of nonlinear wave and diffusion processes with the stepwise change in equation
coefficients in dependence of the solution amplitude and with non-fixed boundaries are …

Purpose This paper aims to study the two-dimensional steady magneto-hydrodynamic flow
of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM) …

In this work, a modified form of Taylor series is proposed which we call the moving Taylor
series. We prove theorems that formulate coefficients of the proposed series along with the …

The wave equation with the stepwise nonlinear coefficient on the semi-axis is considered.
The boundary problems allowing to obtain the exact solutions of such nonlinear wave …