On mittag-leffler type function, fractional calculas operators and solutions of integral equations

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Abstract
The special entire function of the form with is introduced, where α>0, m>0 and α(im+1)+1≠ 0,−1, −2,.....for i=0,1,2,....For m = 1, Eα1,l(z) coincides with the Mittag-Leffler function Eα,α+1 ,with exactness to the constant multiplier γ(αl+1)The connections of Eα,m,l(z) with the Riemann-Liouville fractional integrals and derivatives are investigated and their applications to solving the linear Abel-Volterra integral equations are given.

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