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ON SOME PROPERTIES OF THE GENERALIZED Q-MITTAG-LEFFLER FUNCTION

K. Sharma
장전수학회 (Jangjeon Mathematical Society)|2015.01|Advanced Studies in Contemporary Mathematics|제25권 제1호|pp. 65-73

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참고문헌

키워드

fractional integralfractional derivativeq-exponential functionq- integralq- deriva- tiveq-Mittag-Leer functionMittag-Leer functiongeneralized Mittag-Leer function
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초록

In this paper, the author has introduced q-analogues of gen- eralized Mittag-Leer function referred earlier by Prabhakar[18]. Re- sults derived in this paper are the extensions of the results derived earlier by Annaby et al.[12]. Some special cases are also discussed.

Abstract

In this paper, the author has introduced q-analogues of gen- eralized Mittag-Leer function referred earlier by Prabhakar[18]. Re- sults derived in this paper are the extensions of the results derived earlier by Annaby et al.[12]. Some special cases are also discussed.

참고문헌 (19)

  1. Adders Wiman, "Uber die Nullsteliun der Fuctionen E (x)", Acta Math, 29, pp.217~234
  2. G. Bangerezako, "Variational calculus on q-nonuniform lattices", J. Math. Anal. Appl, 306(1), pp.161~179 (2005)
  3. G. Gasper, "Encyclopedia of Math. And its Appl. 96" (2004), Cambridge University Press
  4. G. Gasper, "Basic hypergeometric series" (1990), Cambridge University Press
  5. G.M.Mittag-Leffler, "Sur la nuovelle function E(x)", C.R. Acad. Sci. Paris, 137, pp.554~558 (1903)
  6. G. M. Mittag-Leffler, "Sur la representation analytique deune branche uniforme une function monogene", Acta. Math, 29, pp.101~181 (1905)
  7. I. Podlubny, "Fractional Di erential Equations(An Introduction to Fractional Derivatives, Fractional di erential Equations, Some Methods of Their Solution and Some of Their Applications)" (1999), Academic Press
  8. Jian-Ping Fang, "SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR", 대한수학회지, 47(2), pp.223~233 (2010), 대한수학회
  9. K.Sharma, "q-fractional initial value problem and q-analogue of generalized Mittag-Leffler function", J. Sci. Arts, 4(21), pp.431~438 (2012)
  10. K.Sharma, "q-fractional integrals and special functions", Adv. Std. Conemp. Math, 24(1), pp.87~95 (2014)
  11. M.H. Abu-Risha, "Linear q-di erence equations", Z. Anal. Anwend, 26, pp.481~494 (2007)
  12. M.H. Annaby, "q-Calculus and Equations", pp.1~340 (2012), Springer-Verlag
  13. P.M.Rajkovic, "On q-Analogues of Caputo Derivative and Mittag-Leffler Function", Fract. Calc. Appl. Anal, 10(4), pp.359~373 (2007)
  14. R.P.Agarwal, "Certain fractional q-integrals and q-derivatives", Proc. Camb. Phil. Soc, 66, pp.365~370 (1969)
  15. S.D. Purohit, "Summation formulae for basic hypergeometric functions via fractional q-calculus", Le Mathematiche, 64(1), pp.67~75 (2009)
  16. T. Abdeljawad, "A generalized q-Mittag-Leer function by q Caputo fractional linear equations", Abst. Appl. Anal, pp.1~11 (2012)
  17. T. Ernst, "A method for q-calculus", J. Nonlinear Math. Phys., 10(4), pp.487~525 (2003)
  18. T.R. Prabhakar, "A Singular Integral Equation with a Generalized Mittag-Leer Function in the Kernel", Yokohama Math. J., 19, pp.7~15 (1971)
  19. Z.S.I. Mansour, "Linear sequential q-difference equations of fractional order", Frac. Calc. Appl. Anal., 12(2), pp.159~178 (2009)

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