Homotopy analysis method for solving multi-term linear and nonlinear diffusion–wave equations of fractional order

Jafari, Hossein; Golbabai, A.; Seifi, Saeed; Sayevand, Khosro

doi:10.1016/j.camwa.2009.06.020

Cited by 64 publications

(21 citation statements)

References 12 publications

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“…The HAM has been successfully applied by many researchers for solving linear and nonlinear partial differential equations. [14][15][16][17][18][19][20][21][22] In recent years, many researchers have paid attention to obtaining solutions to linear and nonlinear differential and integral equations using various methods by combining the Laplace transform method. Among these, we may mention the following: Laplace decomposition methods 23,24 and homotopy perturbation transform method.…”

Section: Introductionmentioning

confidence: 99%

A modified homotopy analysis method for solution of fractional wave equations

Yin

Kumar

2015

Advances in Mechanical Engineering

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The aim of this article is to introduce a modified analytical approach to obtain quick and accurate solution of wave-like fractional physical models. This modified analytical approach is an innovative adjustment in Laplace transform algorithm and homotopy analysis method for fractional partial differential equations. The proposed technique solves the problems using Adomian's polynomials. The homotopy analysis transform method utilizes a simple and powerful method to adjust and control the convergence region of the infinite series solution using an auxiliary parameter. The numerical solutions obtained by this modified proposed method indicate that the approach is easy to implement, highly accurate, and computationally very attractive. A good agreement between the obtained solutions and some well-known results has been obtained.

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Section: Introductionmentioning

confidence: 99%

A modified homotopy analysis method for solution of fractional wave equations

Yin

Kumar

2015

Advances in Mechanical Engineering

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“…Some semi-analytic methods have also been employed to explore series solution for fractional order PDEs. These included homotopy analysis method [5], Adomian decomposition method [6,7], homotopy perturbation method [8], variational iteration method [9], and fractional differential transformation method [10].…”

Section: Introductionmentioning

confidence: 99%

A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

et al. 2019

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The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h 4 + t 2 ) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature.

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“…The homotopy analysis transform method (HATM) is coupling of homotopy analysis method (HAM) [36][37][38][39] and the well-known Laplace transform, provides more realistic solutions that converge very rapidly in real physical problems. HATM is used to modulate HAM, thereafter di erent approaches have been applies to FDDEs design problems and evaluate more convenient reliable series solution.…”

Section: Introductionmentioning

confidence: 99%

Numerical computation of fractional Lotka-Volterra equation arising in biological systems

Ramswroop¹,

Singh

Kumar

2015

Nonlinear Engineering

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In this paper, we present the homotopy analysis transform method (HATM) to solve fractional LotkaVolterra equation, which describes the long term servival of species. The HATM solutions, denotes less error compare with their respective exact solution for α = . In addition to non-proposed techniques, HATM is valid for both small and large parameters, it also provides us with a simple way to adjust and control the parameter and auxiliary function H(t), which play e ective role for convergence solutions of fractional di erential-di erence equations (FDDEs).

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Homotopy analysis method for solving multi-term linear and nonlinear diffusion–wave equations of fractional order

Cited by 64 publications

References 12 publications

A modified homotopy analysis method for solution of fractional wave equations

A modified homotopy analysis method for solution of fractional wave equations

A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

Numerical computation of fractional Lotka-Volterra equation arising in biological systems

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