Transmutation Method for Solving Erd´elyi]Kober Fractional Differintegral Equations

By means of fractional calculus techniques we find explicit solutions of Volterra integral equations of the second kind and fractional differential and differintegral equations, involving Erd´elyi]Kober fractional integrals and derivatives. Also, some hypergeometric integral equations have been considered and solved as double Erd´elyi]Kober equations of the second kind. We use the transmutation method to reduce the solutions of all these equations to known solutions of simpler Rie- mann]Liouville. equations of the same type. Some examples are given.