Volume 40, Issue 1 pp. 306-318
Research Article

Stability, periodicity, and symmetries of certain second-order fractional difference equation with quadratic terms via KAM theory

Mirela Garić-Demirović

Mirela Garić-Demirović

Department of Mathematics, University of Tuzla, Tuzla, 75000 Bosnia and Herzegovina

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M. Nurkanović

Corresponding Author

M. Nurkanović

Department of Mathematics, University of Tuzla, Tuzla, 75000 Bosnia and Herzegovina

Correspondence to: M. Nurkanović, Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina

E-mail: [email protected]

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Z. Nurkanović

Z. Nurkanović

Department of Mathematics, University of Tuzla, Tuzla, 75000 Bosnia and Herzegovina

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First published: 16 June 2016
Citations: 3

Abstract

By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation

urn:x-wiley:mma:media:mma4000:mma4000-math-0001
where A,B,D > 0,u−1,u0>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.

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