Fractional differential equations with time varying coefficients and delay are encountered in the analysis of models of metal cutting processes such as milling and drilling with viscoelastic damping elements. Viscoelastic damping is modeled as a fractional derivative. In the present paper, delayed fractional differential equations with bounded time varying coefficients in four different forms are analyzed using series solution and Chebyshev spectral collocation. A fractional differential equation with a known exact solution is then solved by the methodology presented in the paper. The agreement between the two is found to be excellent in terms of point-wise error in the trajectories. Solutions to the described fractional differential equations are computed next in state space and second order forms.
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January 2015
Research-Article
Computing Numerical Solutions of Delayed Fractional Differential Equations With Time Varying Coefficients
Venkatesh Suresh Deshmukh
Venkatesh Suresh Deshmukh
Department of Mechanical Engineering,
e-mail: venkatesh.deshmukh@villanova.edu
Villanova University
,800 Lancaster Avenue
,Villanova, PA 19085
e-mail: venkatesh.deshmukh@villanova.edu
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Venkatesh Suresh Deshmukh
Department of Mechanical Engineering,
e-mail: venkatesh.deshmukh@villanova.edu
Villanova University
,800 Lancaster Avenue
,Villanova, PA 19085
e-mail: venkatesh.deshmukh@villanova.edu
Manuscript received March 5, 2013; final manuscript received April 21, 2014; published online September 12, 2014. Assoc. Editor: Hiroshi Yabuno.
J. Comput. Nonlinear Dynam. Jan 2015, 10(1): 011004 (5 pages)
Published Online: September 12, 2014
Article history
Received:
March 5, 2013
Revision Received:
April 21, 2014
Citation
Suresh Deshmukh, V. (September 12, 2014). "Computing Numerical Solutions of Delayed Fractional Differential Equations With Time Varying Coefficients." ASME. J. Comput. Nonlinear Dynam. January 2015; 10(1): 011004. https://doi.org/10.1115/1.4027489
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