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Mean fractional-order-derivatives differential equations and filters. (English) Zbl 0882.34007
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:
 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 26A33 Fractional derivatives and integrals 45J05 Integro-ordinary differential equations 47E05 General theory of ordinary differential operators