Electron. J. Differential Equations,
Vol. 2017 (2017), No. 280, pp. 117.
Exponential stability of solutions of nonlinear fractionally perturbed
ordinary differential equations
Eva Brestovanska, Milan Medved
Abstract:
The main aim of this paper is to prove a theorem on the exponential stability
of the zero solution of a class of integrodifferential equations,
whose righthand sides involve the RiemannLiouville 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: RiemannLiouville integral; RiemannLiouville 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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