Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions
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  • 作者：Lynn Erbe ; Christopher S Goodrich ; Baoguo Jia…
  • 关键词：26A48 ; 26A51 ; 39A06 ; 39A10 ; 39A22 ; 39A30 ; 39B62 ; 26A33 ; 34D05 ; 39A12 ; 39A30 ; 39A60 ; 39A99 ; 39B99 ; fractional difference calculus ; monotonicity ; convexity ; asymptotic behavior of solution ; fractional initial value problem
  • 刊名：Advances in Difference Equations
  • 出版年：2016
  • 出版时间：December 2016
  • 年：2016
  • 卷：2016
  • 期：1
  • 全文大小：1,963 KB
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  • 作者单位：Lynn Erbe (1)
    Christopher S Goodrich (2)
    Baoguo Jia (3)
    Allan Peterson (1)

    1. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588-0130, USA
    2. Department of Mathematics, Creighton Preparatory School, Omaha, NE, 68114, USA
    3. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
  • 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
  • 出版者：Springer International Publishing
  • ISSN：1687-1847
文摘
In this article we discuss some of the qualitative properties of fractional difference operators. We especially focus on the connections between the fractional difference operator and the monotonicity and convexity of functions. In the integer-order setting, these connections are elementary and well known. However, in the fractional-order setting the connections are very complicated and muddled. We survey some of the known results and suggest avenues for future research. In addition, we discuss the asymptotic behavior of solutions to fractional difference equations and how the nonlocal structure of the fractional difference can be used to deduce these asymptotic properties. Keywords fractional difference calculus monotonicity convexity asymptotic behavior of solution fractional initial value problem

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