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 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 |
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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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