Proper initialization of fractional-order operators has been an ongoing problem, particularly in the application of Laplace transforms with correct initialization terms. In the last few years, a history-function-based initialization along with its corresponding Laplace transform has been presented. Alternatively, an infinite-dimensional state-space representation along with its corresponding Laplace transform has also been presented. The purpose of this paper is to demonstrate that these two approaches to the initialization problem for fractional-order operators are equivalent and that the associated Laplace transforms yield the correct initialization terms and can be used in the solution of fractional-order differential equations.
Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators
Contributed by the Design Engineering Division for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received October 1, 2012; final manuscript received February 1, 2013; published online June 10, 2013. Assoc. Editor: J. A. Tenreiro Machado.
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Hartley, T. T., Lorenzo, C. F., Trigeassou, J., and Maamri, N. (June 10, 2013). "Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators." ASME. J. Comput. Nonlinear Dynam. October 2013; 8(4): 041014. https://doi.org/10.1115/1.4023865
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