Recent Trends of Computational Methods in Vibration Problems.

Journal Article

Hassan, Senhashish Chakraverty, Atma Sahu, Choong Kok Keong, and Saleh M. . 2015

• Publication Work Type: Research work
• Issue Number: 645981
• Volume Number: 1 (2012)
• Pages: 1 to 2

Publication Abstract

This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform
with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractionalDrinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.