Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE DYNAMICS OF POSITIVE SOLUTIONS OF A HIGHER ORDER FRACTIONAL DIFFERENCE EQUATION WITH ARBITRARY POWERS

  • GUMUS, MEHMET (Department of Mathematics, Bulent Ecevit University) ;
  • SOYKAN, YUKSEL (Department of Mathematics, Bulent Ecevit University)
  • Received : 2015.11.20
  • Accepted : 2017.02.24
  • Published : 2017.05.30
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Abstract

The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation $$x_{n+1}=\frac{^{{\alpha}x}n-1(k+1)}{{\beta}+{\gamma}x^p_{n-k}x^q_{n-(k+2)}}$$, $$n=0,1,{\dots}$$ where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-(k+2)}$,$x_{-(k+1)}$, ${\dots}$, $x_{-1}$, $x_0{\in}\mathb{R}^+$.

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References

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