Operational method for solving generalized Abel integral equation of second kind

A modification of the Mikusinski operational calculus is used to obtain explicit solutions of some classes of integral equations of the second kind of Abel type. In particular, the solution of the generalized Abel equation y(x) - (m)(i = 1) Sigma lambda i(I(0+)(alpha i mu)y)(x) = f(x), alpha(i) > 0, 1 less than or equal to i less than or equal to m, mu > 0, x > 0 with the Riemann-Liouville fractional integral operator I-0+(mu) of order mu is expressed in terms of the Mittag-Leffler function of several variables.