Abstract. In this paper we investigate a method for constructing solutions of differential equations of fractional order with Hadamard type derivative. The basis of this method is the construction of systems concerning the operator of fractional differentiation with Hadamard type derivative. We define new classes of special functions generalizing the Mittag-Leffler functions, and related to the differential equations of fractional order. Properties of these functions and their applications to solutions of fractional order differential equations are established. Analytical solutions of differential equations of fractional order are found as a series. Moreover, we consider normed systems of non-homogeneous differential equations of fractional order.

Received: January 21, 2013

AMS Subject Classification: 35J40, 35J05

Key Words and Phrases: fractional derivative, Hadamard operator, normed system, operator method

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