E. N. Ogorodnikov, N. S. Yashagin, “Some Special Functions in the Solution To Cauchy Problem for a Fractional Oscillating Equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2009, Issue 1(18),Pages <nobr>276

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Short Communication
Differential Equations

Some Special Functions in the Solution To Cauchy Problem for a Fractional Oscillating Equation

E. N. Ogorodnikov, N. S. Yashagin

Samara State Technical University; Dept of Applied Mathematics and Computer Science

Abstract: Some special functions, concerning Mittag–Leffler type function, are introduced. The solution to Cauchy problem for some linear non-homogeneous fractional oscillating equation in terms of these functions are given.

Keywords: Mittag-Leffler type function, Rieman-Liouville's franctional integrals and derivates, Caushy problem for a fractional occilating equation.

UDC: 517.968:517.589

MSC: 56U78

Original article submitted 05/X/2008
revision submitted – 12/II/2009

DOI: 10.14498/vsgtu685