<p>In this paper, various classes of nonlinear equations containing Riemann-Liouville fractional integrals are studied. Global theorems on the existence, uniqueness, and estimates of their solutions are proved by the method of monotone (in the Browder-Minty sense) operators in Lebesgue real spaces under uncomplicated restrictions on the nonlinearities and parameters. The corollaries illustrating the obtained results are given.</p>