We focus on a new type of nonlinear integro-differential equations with
nonlocal integral conditions. The considered problem has one
nonlinearity with time variable singularity. It involves also some
convergent series combined to Riemann-Liouville integrals. We prove a
uniqueness of solutions for the proposed problem, then, we provide some
examples to illustrate this result. Also, we discuss the Ulam-Hyers
stability for the problem. Some numerical simulations, using Rung Kutta
method, are discussed too. At the end, a conclusion follows.