Comparison of optimal homotopy analysis method and fractional homotopy analysis transform method for the dynamical analysis of fractional order optical solitons

Abstract

In this article, dynamical analysis of fractional order Schrödinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the solutions obtained by the two asymptotic techniques, that is, the fractional homotopy analysis transform method and the optimal homotopy analysis method is performed to select the most accurate technique for the stated problem.

Weakly resonant double Hopf bifurcation in coupled nonlinear systems with delayed freedback and application of homotopy analysis method

“…Substituting equation (39) into equation (37) and separating the real and imaginary parts, the normal form equations are drawn:…”

“…By taking proper values of the auxiliary and homotopy parameters, its numerical values of the state variables are computed and presented graphically for different particular cases. Fei et al 37 analyzed a sinusoidal excited piecewise linear-nonlinear oscillator, and proposed an approximate solution for the oscillator by using the HAM and matching method. The validity criteria for the application of the semi-analytic asymptotic methods are exploited, 38 comparison between the solutions obtained by the two asymptotic techniques, that is, the fractional homotopy analysis transform method and the optimal HAM is performed to select the most accurate technique for the stated problem.…”

Important Paradigms of the Thermoelastic Waves

“…The key variables are the change in the temperature and the elastic behaviour, which are closely correlated in the literature to the deformation properties of solids. Investigation of the thermoelastic waves has remained a challenge in industry as well as in the field of bio-informatics and bio-manufacturing, plasma physics and in the study of condensed matter [1][2][3][4][5][6][7]22]. In short, the theory of elasticity has remained an important area of research since the elementary methods of strength of materials are insufficient at some scales to provide the detailed insight of the stress distribution and other properties in the domain of structural mechanics.…”

“…During the past decade, enormous efforts have been made to address this requirement and the interaction between magnetic fields and strain in a thermoelastic materials is studied due to its many applications [2,3]. Usually, in these investigations the heat equation under consideration is taken as the uncoupled or the coupled equation [5].…”

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“…Furthermore, they used the same procedure to obtain an approximate solution of nonlinear equations that arise in steady state flow of a fourth-grade fluid past a porous plate, and for the solution of a nonlinear equation arising in heat transfer. OHAM has been successfully employed to solve different kinds of differential equations in science and engineering [18][19][20][21][22][23][24].…”