UNIQUENESS OF SOLUTIONS, STABILITY AND SIMULATIONS FOR A DIFFERENTIAL PROBLEM INVOLVING CONVERGENT SERIES AND TIME VARIABLE SINGULARITIES

We study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series combined with Riemann–Liouville integrals. We prove an existence and uniqueness result for our problem. Some examples are given to illustrate the uniqueness result. The Ulam–Hyers stability for the problem is also studied. Then, thanks to some numerical techniques, that allow us to approximate the Caputo derivatives, and by using the Runge–Kutta method, we present a numerical study with some simulations to show more comprehension of the proposed examples.