Dissipativity and stability for a nonlinear differential equation with distributed order symmetrized fractional derivative (Q2430070)

The authors consider the equation \[ \frac{d^2u}{dt^2}\,(t)+b \int_{0}^{1} {}^{\pm} {\mathcal E}^{\alpha}_{T}u(t) \phi(\alpha) d \alpha + F(u(t))=0,\quad t\in (0,T],\quad u(0)=u_0,\quad \frac{du}{dt}\,(0)= v_0, \] which is a generalization of mathematical models describing oscillations with fractional damping. The equation considered is a nonlinear differential equation with distributed order symmetrized fractional derivative. The authors study criteria for uniqueness, dissipativity and stability of the solutions of the above equation.