Positive solutions of Riemann-Stieltjes integral boundary problems for the nonlinear coupling system involving fractional-order differential

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• 作者：Kaihong Zhao (1)
  Ping Gong (1)
  
  1. Department of Applied Mathematics ; Kunming University of Science and Technology ; Kunming ; Yunnan ; 650093 ; China
  
• 关键词：coupling fractional differential system ; positive solutions ; Riemann ; Stieltjes integral BVPs ; fixed point theorem
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：395 KB
• 参考文献：1. Lakshmikantham, V, Leela, S (2009) Nagumo-type uniqueness result for fractional differential equations. Nonlinear Anal 71: pp. 2886-2889 CrossRef
  2. Chen, F, Zhou, Y (2011) Attractivity of fractional functional differential equations. Comput. Math. Appl 62: pp. 1359-1369 CrossRef
  3. Chang, Y, Nieto, J (2009) Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Model 49: pp. 605-609 CrossRef
  4. Kilbas, AA, Trujillo, JJ (2001) Differential equations of fractional order: methods, results and problems-I. Appl. Anal 78: pp. 153-192 CrossRef
  5. Kilbas, AA, Trujillo, JJ (2002) Differential equations of fractional order: methods, results and problems-II. Appl. Anal 81: pp. 435-493 CrossRef
  6. Bai, Z (2010) On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Anal 72: pp. 916-924 CrossRef
  7. Bai, Z, Qiu, T (2009) Existence of positive solution for singular fractional differential equation. Appl. Math. Comput 215: pp. 2761-2767 CrossRef
  8. Ahmad, B, Nieto, JJ (2009) Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput. Math. Appl 58: pp. 1838-1843 CrossRef
  9. Henderson, J, Luca, R (2014) Existence and multiplicity of positive solutions for a system of fractional boundary value problems. Bound. Value Probl.
  10. Ahmad, B, Ntouyas, S, Alsaedi, A (2011) New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ.
  11. Webb, JRL (2009) Positive solutions of some higher order nonlocal boundary value problems. Electron. J. Qual. Theory Differ. Equ.
  12. Webb, JRL, Infante, G (2009) Nonlocal boundary value problems of arbitrary order. J. Lond. Math. Soc 79: pp. 238-258
  13. Feng, M, Ji, D, Ge, W (2008) Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces. J. Comput. Appl. Math 222: pp. 351-363 CrossRef
  14. Jia, M, Liu, X (2011) Three nonnegative solutions for fractional differential equations with integral boundary conditions. Comput. Math. Appl 62: pp. 1405-1412 CrossRef
  15. Zhang, HE (2014) Multiple positive solutions of nonlinear BVPs for differential systems involving integral conditions. Bound. Value Probl.
  16. Chatthai, T, Jessada, T, Sotiris, KN (2014) Impulsive fractional boundary-value problems with fractional integral jump conditions. Bound. Value Probl.
  17. Kilbas, A, Srivastava, H, Trujillo, J (2006) North-Holland Mathematics Studies 204. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam
  18. Podlubny, I (1993) Fractional Differential Equations. Academic Press, New York
  19. Guo, D, Lakshmikantham, V, Liu, X (1996) Mathematics and Its Applications 373. Nonlinear Integral Equations in Abstract Spaces. Kluwer Academic, Dordrecht CrossRef
  20. Joshi, MC, Bose, RK (1985) Some Topics in Nonlinear Functional Analysis. Wiley Eastern, New Delhi
  
• 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 study Riemann-Stieltjes integral boundary value problems of nonlinear fractional functional differential coupling system involving higher-order Caputo fractional derivatives. Some sufficient criteria are obtained for the existence, multiplicity, and nonexistence of positive solutions by applying fixed-point theorems on a convex cone. As applications, some examples are provided to illustrate our main results.