全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
-  2015 

分数阶微分方程边值问题非平凡解的存在性
Existence of nontrivial solutions for boundary value problems of fractional differential equations

DOI: 10.6040/j.issn.1671-9352.0.2014.317

Keywords: 非平凡解,Leray-Schauder度,分数阶边值问题,
fractional boundary value problem
,Leray-Schauder degree,nontrivial solution

Full-Text   Cite this paper   Add to My Lib

Abstract:

摘要: 运用Leray-Schauder度理论, 在相关算子第一特征值条件下, 获得分数阶微分方程边值问题 非平凡解的存在性, 其中α∈(2,3]是一实数, D0+α 是α阶Riemann-Liouville 分数阶导数。
Abstract: By applying the theory of Leray-Schauder degree, the existence of nontrivial solutions for the boundary value problems of fractional differential equations is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator.Here α∈(2,3]is a real number, D0+α is the standard Riemann-Liouville fractional derivative of order α

References

[1]  YUAN C. Two positive solutions for <em>(n</em>-1,1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations[J]. Commun Nonlinear Sci Numer Simulat, 2012, 17(2):930-942.
[2]  许晓婕, 胡卫敏. 一个新的分数阶微分方程边值问题正解的存在性结果[J]. 系统科学与数学, 2012, 32(5):580-590. XU Xiaojie, HU Weimin. The existence results of positive solutions of a new fractional differential equation of boundary value problems[J]. System Science and Mathematics, 2012, 32(5):580-590.
[3]  EL-SHAHED M. Positive solutions for boundary value problems of nonlinear fractional differential equation[J]. Abs Appl Anal, 2007, 2007(1):1-8.
[4]  YANG X, WEI Z, DONG W. Existence of positive solutions for the boundary value problem of nonlinear fractional differential equations[J]. Commun Nonlinear Sci Numer Simulat, 2012, 17(1):85-92.
[5]  郑祖庥.分数微分方程的发展和应用[J].徐州师范大学学报, 2008, 26(2):1-10. ZHENG Maxiu. Development and applications of fractional differential equations[J]. Jounal of Xuzhou Nomal University, 2008, 26(2): 1-10.
[6]  GUO D, LAKSHMIKANTHAM V. Nonlinear problems in abstract cones[M]. Orlando: Academic Press, 1988.
[7]  BAI Z. On positive solutions of a nonlocal fractional boundary value problem[J]. Nonlinear Analysis, 2010, 72(2):916-924.
[8]  XU J, YANG Z. Multiple positive solutions of a singular fractional boundary value problem[J]. Applied Mathematics E-Note, 2010, 10:259-267.
[9]  XU J, WEI Z, DONG W. Uniqueness of positive solutions for a class of fractional boundary value problem[J]. Appl Math Lett, 2012, 25(3):590-593.
[10]  LI Q, SU H, WEI Z. Existence and uniqueness result for a class of sequential fractional differential equations[J]. J Appl Math Comput, 2012, 38(1/2):641-652.
[11]  SAMKO S, KILBAS A, MARICHEV O. Fractional integrals and derivatives: theory and applications,gordon and breach[M]. London: Taylor and Francis Ltd, 1993.
[12]  PODLUBNY I. Fractional differential equations, in: mathematics in science and engineering[M]. New York: Academic Press, 1999.
[13]  FENG W, SUN S, HAN Z, et al.Existence of solutions for a singular system of nonlinear fractional differential equations[J]. Comput Math Appl, 2011, 62(3):1370-1378.
[14]  XU Jiafa, WEI Zhongli, DING Youzheng. Positive solutions for a boundary-value problem with Riemann-Liouville fractional derivative[J]. Lithuanian Mathematical Journal, 2012, 52(4):462-476.
[15]  NUSSBAUM R. Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem in fixed point theory[J]. Lecture Notes in Math, 1981, 886:309-330.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133