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Entropy 2015, 17(10), 6925-6936; doi:10.3390/e17106925

Modified Legendre Wavelets Technique for Fractional Oscillation Equations

1
Department of Mathematics, Faculty of Sciences, HITEC University, 47080 Taxila, Pakistan
2
Department of Mathematics, College of Science, King Saud University, 2455 Riyadh 11451, Kingdom of Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 22 July 2015 / Revised: 10 September 2015 / Accepted: 15 September 2015 / Published: 16 October 2015
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory)
View Full-Text   |   Download PDF [744 KB, uploaded 16 October 2015]   |  

Abstract

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques. View Full-Text
Keywords: Legendre wavelets method; Picard’s iteration; nonlinear problems; fractional oscillation equations Legendre wavelets method; Picard’s iteration; nonlinear problems; fractional oscillation equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Mohyud-Din, S.T.; Iqbal, M.A.; Hassan, S.M. Modified Legendre Wavelets Technique for Fractional Oscillation Equations. Entropy 2015, 17, 6925-6936.

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