Geodesic
Fractional Integration and Fractional Differentiation of the M-Series
Fractional calculus and applied analysis, Tome 11 (2008) no. 2, pp. 187-191.

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In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the Mittag-Leffler function occurs as solution of fractional integral equations in those area. In this short note we have obtained formulas for the fractional integral and fractional derivative of the M-series.
Keywords: Fractional Calculus Operators, Special Functions, 26A33, 33C60, 44A15 
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Sharma, Manoj. Fractional Integration and Fractional Differentiation of the M-Series. Fractional calculus and applied analysis, Tome 11 (2008) no. 2, pp. 187-191. http://geodesic.mathdoc.fr/item/FCAA_2008_11_2_a6/