IJPAM: Volume 84, No. 4 (2013)
DIFFERENTIAL EQUATIONS OF FRACTIONAL
ORDER WITH A HADAMARD TYPE OPERATOR
1,2Department of Mathematics
University named after A. Yasawi
Turkestan, 161200, REPUBLIC OF KAZAKHSTAN
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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DOI: 10.12732/ijpam.v84i4.13 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395