Applications of Laplace Homotopy Analysis Method for Solving Fractional Heat-And Wave-like Equations

Pramod Kumar; Dr. V.G.Gupta

Applications of Laplace Homotopy Analysis Method for Solving Fractional Heat-And Wave-like Equations

Pramod Kumar * §

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Dr. V.G.Gupta

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§ Jaipur National University, Jaipur.

Applications of Laplace Homotopy Analysis Method for Solving Fractional Heat-And Wave-like Equations

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Abstract

In this paper, we apply Laplace homotopy analysis method for solving various fractional heat-and wave-like equations. This method is combined form of homotopy analysis method and Laplace transform. The proposed algorithm presents a procedure of construct the base function and gives a high order deformation equation in simple form. The purpose of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in the other analytical techniques. Numerical examples demonstrate the capability of LHAM for fractional partial differential equations.

References

33 Cites in Article

Reference Format

Adel Al-Rabtah,Vedat Ertürk,Shaher Momani (2010). Solutions of a fractional oscillator by using differential transform method.
F Mainardi (1997). Fractional Calculus.
G Draganescu (2006). Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives.
G Pukhov (1978). Computational structure for solving differential equations by Taylor transformations.
H Arora,F Abdelwahid (1993). Solution of non-integer order differential equations via the Adomian decomposition method.
H Jafari,V Daftardar-Gejii (2006). Solving linear and non-linear fractional diffusion and wave equations by Adomian-decomposition.
I Podlubny,M Kacenak (1999). Isoclinal matrices and numerical solution of fractional differential equations.
Jie Cang,Yue Tan,Hang Xu,Shi-Jun Liao (2007). Series solutions of non-linear Riccati differential equations with fractional order.
J He (1999). Homotopy perturbation technique.
Qingqing Chai,Dandan Wu,Fan Liu,Fei Song,Xibiao Tang,Yun Cao,Qigai He (1986). Therapy Potential of Tailless Bacteriophage ΦHN161 and its Ability in Modulating Inflammation Caused by Bacterial Disease.
K Oldham,J Spanier (1974). The fractional calculus.
K Miller,B Ross (1993). Introduction to Fractional Calculus.
Lina Song,Hongqing Zhang (2007). Application of homotopy analysis method to fractional KdV–Burgers–Kuramoto equation.
M Caputo (1967). Linear models of dissipation whose Q is almost frequency independent. Part III.
M Yulita,M Noorani,I Hashim (2009). Variational iteration method for fractional heat-and wave -like equations.
M Zurigat (2011). Solving fractional oscillators using Laplace homotopy analysis method.
R Gorenflow,F Mainardi (1997). Fractional Calculus: integral and differential equations of fractional order.
W Schneider,W Wyss (1989). Fractional diffusion and wave equations.
Wenbo Xie,Xu Peng,Hongmei Jiang,Shaopeng Lu,Yongmin Gu,Chien-Pin Chen,Qiang Zhang (1992). Experimental Study of Turbine Blade Tip Heat Transfer with High-Speed Relative Casing Motion.
Shi-Jun Liao (1995). An approximate solution technique not depending on small parameters: A special example.
S Liao (1997). A kind of approximate solution technique which does not depend upon small parameters-II. application in fluid mechanics.
S Liao (2003). Introduction.
Shaher Momani,Kamel Al-Khaled (2005). Numerical solutions for systems of fractional differential equations by the decomposition method.
S Momani (2005). Analytic approximate solution for fractional heat-like and wavelike equations with variable coefficients using the decomposition method.
Shaher Momani,Zaid Odibat (2007). Homotopy perturbation method for nonlinear partial differential equations of fractional order.
V Daftardar-Giejji,H Jafari (2007). Solving a multi order fractional differential equations using Adomian decomposition.
V Gupta,S Gupta (2011). Applications of homotopy perturbation transform method for solving heat like and wave like equations with variable coefficients.
Y Bourermel (2007). Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method.
Y Khan,Q Wu (2011). Homotopy perturbation transform method for non-linear equations using He's polynomial.
Y Luchko,R Gorenflow (1998). The initial value problem for some fractional differential equations with the caputo derivatives.
Y Wu,C Wang,S Liao (2004). Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method.
Ζ Odibat,S Momani (2006). Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order.
Z Odibat,S Momani (2007). Numerical comparison of methods for solving linear differential equations of fractional order.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

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Not applicable for this article.

How to Cite This Article

Pramod Kumar, Dr. V.G.Gupta. 2012. "Applications of Laplace Homotopy Analysis Method for Solving Fractional Heat-And Wave-like Equations". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 12 (GJSFR Volume 12 Issue F6).

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GJSFR Volume 12 Issue F6

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

fractional heat- and wave-like equations homotopy analysis method Laplace homotopy analysis method

Classification

GJSFR-F Classification MSC 2010: 80A20

Submission ReceivedApril 6, 2012
Peer Review Double Blind
Handling Editor
Accepted April 28, 2012
Published May 12, 2012

Version of record

v1.2

Issue date

June 16, 2012

Language

English

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Article Matrices

Total Score: 151

Country: India

Subject: Global Journal of Science Frontier Research

Authors: Dr. V.G.Gupta, Pramod Kumar (PhD/Dr. count: 1)

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Publish Date: 2012 05, Sat

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