Modified Legendre Wavelets Technique for Fractional Oscillation Equations
Hassan, 20. Syed Tauseef Mohyud-Din, Muhammad Asad Iqbal, and Saleh M. . 2015
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.
This article is dedicated to analyzing the heat transfer in the flow of water-based nanofluids in a channel with non-parallel stretchable walls. The magnetohydrodynamic (MHD) nature of the flow is…
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…
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