The homotopy analysis method for handling systems of fractional differential equations

Zurigat, Mohammad; Momani, Shaher; Odibat, Zaid; Alawneh, Ahmad

doi:10.1016/j.apm.2009.03.024

Cited by 121 publications

(76 citation statements)

References 25 publications

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“…Compared to other numerical and non-numerical techniques, HAM provides a convenient way to control and adjust the convergence region of the solution series. The application of HAM has been demonstrated to a variety of problems arising from science and engineering for all types of boundary and initial conditions governed by nonlinear equations involving both integer and fractional order derivatives [6,[9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, the HAM is extended to solve many nonlinear fractional differential equations (see [6,[17][18][19][20][21][22][23] and the references there).…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Bakkyaraj

Sahadevan

2015

Int. J. Appl. Comput. Math

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In this article, we consider the well known nonlinear Schrödinger equation (NLS) with fractional time derivative and derive its approximate analytical solution using the homotopy analysis method (HAM). We also applied HAM to two coupled time fractional NLS and constructed its approximate solution. The question of convergence of the obtained solution is discussed. The obtained approximate analytical periodic wave solution, solitary wave solution and the effect of time fractional order α are shown graphically.

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Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Bakkyaraj

Sahadevan

2015

Int. J. Appl. Comput. Math

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“…In particular, the method has found a number of applications in heat conduction problems [1,16,18,26,56]. It is also used, among others, for solving the nonlocal initial boundary value problem [35], nonlinear reaction-diffusion-convection problems [41] and fractional differential equations [4,54,58]. In several papers the method was used for solving the integro-differential equations [9,14,20,43,57].…”

Section: Introductionmentioning

confidence: 99%

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

et al. 2013

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The paper presents an application of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind. In this method a series is created, sum of which (if the series is convergent) gives the solution of discussed equation. Conditions ensuring convergence of this series are presented in the paper. Error of approximate solution, obtained by considering only partial sum of the series, is also estimated. Examples illustrating usage of the investigated method are presented as well, including the example having practical application for calculating the charge in supply circuit of flash lamps used in cameras.

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“…In this paper, we use the Lie symmetry group method to investigate the following nonlinear system of fractional differential equations [31]:…”

Section: Introductionmentioning

confidence: 99%

Lie group method and fractional differential equations

Zedan¹,

Abu-Nawas²

2017

J. Nonlinear Sci. Appl.

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The homotopy analysis method for handling systems of fractional differential equations

Cited by 121 publications

References 25 publications

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

Lie group method and fractional differential equations

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