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S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.

has been cited by the following article:

Article

Numerical Simulation of Time-fractional Fourth Order Differential Equations via Homotopy Analysis Fractional Sumudu Transform Method

1Department of Mathematics, Jaypee University of Engineering and Technology, Guna, INDIA


American Journal of Numerical Analysis. 2015, Vol. 3 No. 3, 52-64
DOI: 10.12691/ajna-3-3-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
Rishi Kumar Pandey, Hradyesh Kumar Mishra. Numerical Simulation of Time-fractional Fourth Order Differential Equations via Homotopy Analysis Fractional Sumudu Transform Method. American Journal of Numerical Analysis. 2015; 3(3):52-64. doi: 10.12691/ajna-3-3-1.

Correspondence to: Hradyesh  Kumar Mishra, Department of Mathematics, Jaypee University of Engineering and Technology, Guna, INDIA. Email: hk.mishra@juet.ac.in

Abstract

The work provides an incipient analytical technique called the Homotopy Analysis Fractional Sumudu Transform Method (HAFSTM) for solving time-fractional fourth order differential equations with variable coefficients. The HAFSTM is the cumulation of the homotopy analysis method (HAM) and sumudu transform method (STM). The numerical simulation of the proposed method has the sundry applications, it can solve linear and nonlinear boundary value quandaries without utilizing Adomian polynomial, and He’s polynomial, which can be considered a clear advantage of this incipient algorithm. The solutions obtained by proposing technique are very lucid and less computationally implementable.

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