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Article

Multiple Time Scales Solution of an Equation with Quadratic and Cubic Nonlinearities Having Fractional- Order Derivative

by
Fadime Dal
Department of Mathematics, Ege University, Izmir, Turkey
Math. Comput. Appl. 2011, 16(1), 301-308; https://doi.org/10.3390/mca16010301
Published: 1 April 2011
Versions Notes

Abstract

Nonlinear vibrations of quadratic and cubic system are considered. The equation of motion includes fractional order term. Multiple time scales (a perturbation method) solution of the system is developed. Effect of fractional order derivative term is discussed.
Keywords: Fractional differential equation; Caputo fractional derivative; Nonlinear vibrations; Multiple time Scales method Fractional differential equation; Caputo fractional derivative; Nonlinear vibrations; Multiple time Scales method

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MDPI and ACS Style

Dal, F. Multiple Time Scales Solution of an Equation with Quadratic and Cubic Nonlinearities Having Fractional- Order Derivative. Math. Comput. Appl. 2011, 16, 301-308. https://doi.org/10.3390/mca16010301

AMA Style

Dal F. Multiple Time Scales Solution of an Equation with Quadratic and Cubic Nonlinearities Having Fractional- Order Derivative. Mathematical and Computational Applications. 2011; 16(1):301-308. https://doi.org/10.3390/mca16010301

Chicago/Turabian Style

Dal, Fadime. 2011. "Multiple Time Scales Solution of an Equation with Quadratic and Cubic Nonlinearities Having Fractional- Order Derivative" Mathematical and Computational Applications 16, no. 1: 301-308. https://doi.org/10.3390/mca16010301

APA Style

Dal, F. (2011). Multiple Time Scales Solution of an Equation with Quadratic and Cubic Nonlinearities Having Fractional- Order Derivative. Mathematical and Computational Applications, 16(1), 301-308. https://doi.org/10.3390/mca16010301

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