Electron. J. Differential Equations, Vol. 2017 (2017), No. 280, pp. 1-17.

Exponential stability of solutions of nonlinear fractionally perturbed ordinary differential equations

Eva Brestovanska, Milan Medved

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.

Submitted May 5, 2017. Published November 10, 2017.
Math Subject Classifications: 34A08, 34A12, 34D20, 37C75.
Key Words: Riemann-Liouville integral; Riemann-Liouville derivative; Caputo derivative; fractional differential equation; exponential stability.

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Eva Brestovanska
Department of Economics and Finance
Faculty of Management
Comenius University, Odbojarov 10
831 04 Bratislava, Slovakia
email: Eva.Brestovanska@fm.uniba.sk
Milan Medved
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University, 842 48 Bratislava, Slovakia
email: Milan.Medved@fmph.uniba.sk

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