Exponential stability of solutions of nonlinear fractionally perturbed ordinary differential equations
Texas State University, Department of Mathematics
The main aim of this paper is to prove a theorem on the exponential stability of the zero solution of a class of integro-differential equations, whose right-hand sides involve the Riemann-Liouville fractional integrals of different orders and we assume that they are polynomially bounded. Equations of that type can be obtained e.g. from fractionally damped pendulum equations, where the fractional damping terms depend on the Caputo fractional derivatives of solutions. The set of initial values of solutions that converge to the origin is also determined. We also prove an existence and uniqueness theorem for this type of equations, which we use in the proof of the stability theorem.
Riemann-Liouville integral, Riemann-Liouville derivative, Caputo derivative, Fractional differential equation, Exponential stability
Brestovanska, E., & Medved, M. (2017). Exponential stability of solutions of nonlinear fractionally perturbed ordinary differential equations. <i>Electronic Journal of Differential Equations, 2017</i>(280), pp. 1-17.