Fractional Calculus Operators Special Functions 26A33 33C60 44A15
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 11, No 2, (2008), 187p-191p
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.