Some properties of the Mittag-Leffler functions and their relation with the Wright functions

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Kurulay M., Bayram M.

ADVANCES IN DIFFERENCE EQUATIONS, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1186/1687-1847-2012-181
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Mittag-Leffler functions, the Wright functions
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

This paper is a short description of our recent results on an important class of the so-called Mittag-Leffler functions, which became important as solutions of fractional order differential and integral equations, control systems and refined mathematical models of various physical, chemical, economical, management and bioengineering phenomena. We have studied the Mittag-Leffler functions as their typical representatives, including many interesting special cases that have already proven their usefulness in fractional calculus and its applications. We obtained a number of useful relationships between the Mittag-Leffler functions and the Wright functions. The Wright function plays an important role in the solution of a linear partial differential equation. The Wright function, which we denote by W(z; alpha, beta), is so named in honor of Wright who introduced and investigated this function in a series of notes starting from 1933 in the framework of the asymptotic theory of partitions.