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Zbl 0882.34007
Caputo, Michele
Mean fractional-order-derivatives differential equations and filters. (English)
[J] Ann. Univ. Ferrara, Nuova Ser., Sez. VII 41, 73-84 (1995). ISSN 0430-3202; ISSN 1827-1510/e

Summary: The solution of differential equations of fractional order is generalized to the case when the fractional order derivatives are integrated with respect to the order of differentiation. The formal solution is found by means of the Laplace transform. The solutions of the integro-differential equations, defined by means of derivatives of fractional order and of their integrals with respect to the order of differentiation, are also discussed in terms of filtering.

MSC 2000:: *34A25 Analytical theory of ODE
26A33 Fractional derivatives and integrals (real functions)
45J05 Integro-ordinary differential equations
47E05 Ordinary differential operators

Keywords: differential equations of fractional order; formal solution; Laplace transform; integro-differential equations; filtering

Cited in: Zbl 1184.92038

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