الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The name of the fractional calculus does not mean the calculus of fractions. Neither does it mean a fraction of any calculus-differential, integral or calculus of variations. The Fractional Calculus is a name for the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration. The theory of derivatives of non-integer order goes back to the leibniz’s note [12] in his list to L’Hospital, dated 30 september 1695, in which the meaning of the derivative of order one half is discussed. Leibniz’s note led to the appearance of the theory of derivatives and integrals of arbitrary order, which by the end of the XIX century took more or less finished form due primarily to liouville, Grunwald, letnikov, and Riemann. Surveys of the history of the theory of fractional derivatives can be found in [17], [10], [22].