期刊文献+

一类具参数的分数阶差分方程边值问题解的存在唯一性 被引量:1

Existence and Uniqueness of Solutions of Boundary Value Problems for Fractional Order Difference Equations with a Parameter
下载PDF
导出
摘要 研究了阶数介于3到4之间的一类分数阶差分方程的边值问题。通过构造相应的Green函数,证明Green函数的正性性质,利用Banach压缩映像原理和Brouwer不动点定理,在合适的条件下,获得了边值问题解的存在唯一性。特别地,当阶数v=4时,原问题变为整数阶差分方程边值问题,研究结果表明,分数阶差分方程边值问题与整数阶差分方程边值问题具有本质区别。 This paper is concerned with boundary value problems of fractional difference equations with the order between 3 to 4. Green function is technically constructed, the positivity of Green function is obtained. Under the suitable conditions, the existence and uniqueness of solutions of boundary value problems for fractional order difference equations with a parameter is proved by using of Banach contraction mapping principle and Brouwer fixed point theorem. In particular, the difference between fractional order difference equations and integer order difference equations is found, which is significant on research of fractional order difference equations.
出处 《合肥学院学报(综合版)》 2016年第4期5-10,共6页 Journal of Hefei University:Comprehensive ED
基金 国家自然科学基金(11401002 11301004) 安徽省自然科学基金(1508085QA01) 安徽省高校自然科学重点研究项目(KJ2014A010) 安徽省高等教育质量工程项目(2015jyxm057) 安徽大学质量提升计划项目(ZLTS2015052)资助
关键词 分数阶差分方程 GREEN函数 BROUWER不动点定理 压缩映象原理 fractional order difference equation Green function Brouwer fixed point theorem contraction mapping principle
  • 相关文献

参考文献8

  • 1郑祖庥.分数微分方程的发展和应用[J].徐州师范大学学报(自然科学版),2008,26(2):1-10. 被引量:49
  • 2程金发.分数阶差分方程[M].厦门:厦门大学出版社,2010.
  • 3Atici F M, Sengul S. Modeling with Fractional Equations [J]. J Math Anal Appl,2010,369: 1-9.
  • 4Wu F. Nabla Fractional Calculus and Its Application in Analyzing Tumor Growth of Cancer, Master Thesis [ D] . Kentucky:Western University, 2012.
  • 5Goodrich C S. Continuity of Solutions to Discrete Fractional Initial Value Problems [ J]. Computers and Mathematics with Ap-plications, 2010,59(11), 3489-3499.
  • 6Atici F M,Eloe P W. Two-point Boundary Value Problems for Finite Fractional Difference Equations [ J] . Differential Equa-tions and Applications, 2011,17(4) : 445-456.
  • 7Guo D, Lakshimikantham V. Nonlinear Problems in Abstract Cones [ M]. New York: Academic Press, 1988.
  • 8Goodrich C S. Existence and Uniqueness of Solutions to a Fractional Difference Equation with Nonlocal Conditions [ J]. Com-puters and Mathematics with Applications, 2011,61(2) : 191-201.

二级参考文献56

  • 1徐明瑜,谭文长.中间过程、临界现象——分数阶算子理论、方法、进展及其在现代力学中的应用[J].中国科学(G辑),2006,36(3):225-238. 被引量:34
  • 2Miller K S,Ross B. An introduction to the fractional calculus and fractional differential equations[M]. New York: John Wiley & Sons, 1993.
  • 3Podlubny I. Fractional differential equations[M]. San Diego:Acad Press,1999.
  • 4Samko S G,Kilbas A A,Maritchev O I. Integrals and derivatives of the fractional order and some of their applications[M]. Minsk: Naukai Tekhnika, 1987.
  • 5Benchohra M, Henderson J, Ntouyas S K,et al. Existence results for fractional order functional differential equations with infinite delay[J]. J Math Anal Appl,2008,338(2) :1340.
  • 6Oldham K B,Spanier J. The fractional calculus[M]. New York:Acad Press,1974.
  • 7Kiryakova V. Generalized fractional calculus and applications[G]//Pitman Research Notes in Math:301. Harlow: Longman, 1994.
  • 8Blair G W S. Some aspects of the search for invariants[J]. Br J for Philosophy of Sci,1950,1(3):230.
  • 9Blair G W S. The role of psychophysics in theology[J]. J of Colloid Sci,1947(2) -21.
  • 10Westerlund S. Dead matter has memory! [J]. Physica Scripta, 1991,43 : 174.

共引文献48

同被引文献2

引证文献1

二级引证文献1

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部