Dear Jamaleddin

May be next book help you

Gorenflo R., Kilbas A.A., Mainardi F., Rogosin S.V., Mittag-Leffler Functions, Related Topics and Applications (Springer, New York, 2014) 443 pages ISBN 978-3-662-43929-6

S[ncerely Yuri

I think you have problem with term by term integration, if this is problem, you must calculate integrals of type: int((1-\xi)^a*\xi^(1/2)), this is beta function beta(3/2,a) for real(a)>-1. another way: change variable \xi=y^2, then you must calculate integrals of form int((1-y^2)^a*y^2) which can be expressed in terms gamma function.