Analytical properties and applications of the Wright function

Details Analytical properties and applications of the Wright function Analytical properties and applications of the Wright function

2007-01-28

arxiv.org/abs/math-ph/0701069v1

Fractional Calculus and Applied Analysis, Vol. 2 No 4 (1999) 383-414

Physics

Mathematical Physics

34 pages. 3rd Workshop TMSF (Transform Methods and Special Functions)Sofia, Bulgaria, 1999

Scientific paper

In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional diffusion-wave equation can be represented in terms of the Wright function. Furthermore, extending the methods of Lie groups in partial differential equations to the partial differential equations of fractional order it was shown that some of the group-invariant solutions of these equations can be given in terms of the Wright and the generalized Wright functions.Finally, we discuss recent results about distribution of zeros of the Wright function, its order, type and indicator function.

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