Long-time behavior of bounded global solutions to systems of nonlinear integro-differential equations

We study the long-time behavior of bounded solutions of certain systems of nonlinear integro-differential equations, including differential equations of fractional order between 1 and 2. We obtain appropriate Lyapunov functions for this system and prove that any bounded global solution converges to a steady state if the nonlinear potential E occurring in the system satisfies the Łojasiewicz inequality.