Title: Infinite State and Fractional Differentiation of Functions
Abstract:In this chapter, the authors define the initial conditions of the Caputo derivative in the context of fractional differential system transients. In order to express the fractional derivative, they cal...In this chapter, the authors define the initial conditions of the Caputo derivative in the context of fractional differential system transients. In order to express the fractional derivative, they calculate the Caputo derivative on an infinite interval. Practically, the derivative is calculated on a truncated interval. The authors demonstrate that the Caputo derivative of the truncated function converges asymptotically towards the exact value, with a long memory transient. They also demonstrate the interest of the infinite state approach for the calculation of the fractional derivative of a function, i.e. the distributed model of the fractional integrator makes it possible to calculate this fractional derivative using the Caputo derivative definition. Fractional derivatives with the distributed model associated with the Riemann–Liouville derivative can be calculated. More surprisingly, the implicit derivative can also be used.Read More
Publication Year: 2019
Publication Date: 2019-08-05
Language: en
Type: other
Indexed In: ['crossref']
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