Cylindrically symmetric fractional Helmholtz equation is analytically solved in an isotropic medium. The solution approach is based on the Caputo fractional derivatives. The general solution is based on fractional Bessel function attached to particular azimuthal and longitudal exponents. It is expanded in orthogonal basis and represented as complete set as well. Our solution could be used to theoretically describe fractional modes of Bessel Light as well as time-independent fractional diffusion.