Successively iterative method for a class of high-order fractional differential equations with multi-point boundary value conditions on half-line

详细信息    查看全文

• 作者：Bingxian Li ; Shurong Sun ; Zhenlai Han
• 关键词：34A08 ; 34B18 ; Caputo fractional derivative ; multi ; point boundary value problem ; monotone iteration method ; infinite interval ; existence of solutions
• 刊名：Boundary Value Problems
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,585 KB
• 参考文献：1. Oldham, K, Spanier, J: The Fractional Calculus. Academic Press, New York (1974) MATH
  2. Miller, K, Ross, B: An Introduction to the Fractional Calculus and Fractional Differential Equation. Wiley, New York (1993)
  3. Podlubny, I: Fractional Differential Equations. Academic Press, San Diego (1999) MATH
  4. Kilbas, A, Srivastava, H, Trujillo, J: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) MATH
  5. Samko, S, Kilbas, A, Marichev, O: Fractional Integral and Derivative, Theory and Applications. Gordon and Breach, Yverdon (1993)
  6. Zeidler, E: Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorems. Springer, Berlin (1985) CrossRef
  7. Zhai, C, Xu, L: Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter. Commun. Nonlinear Sci. Numer. Simul. 19, 2820-2827 (2014) MathSciNet CrossRef
  8. Li, B, Sun, S, Li, Y: Multi-point boundary value problems for a class of Riemann-Liouville fractional differential equations. Adv. Differ. Equ. 2014, 151 (2014) CrossRef
  9. Zhao, Y, Sun, S, Han, Z, Zhang, M: Positive solutions for boundary value problems of nonlinear fractional differential equations. Appl. Math. Comput. 217, 6950-6958 (2011) MATH MathSciNet CrossRef
  10. Yan, R, Sun, S, Lu, H, Zhao, Y: Existence of solutions for fractional differential equations with integral boundary conditions. Adv. Differ. Equ. 2014, 25 (2014) MathSciNet CrossRef
  11. Yan, R, Sun, S, Sun, Y, Han, Z: Boundary value problems for fractional differential equations with nonlocal boundary conditions. Adv. Differ. Equ. 2013, 176 (2013) MathSciNet CrossRef
  12. Zhao, X, Ge, W: Unbounded solutions for a fractional boundary value problems on the infinite interval. Acta Appl. Math. 109, 495-505 (2010) MATH MathSciNet CrossRef
  13. Su, X: Solutions to boundary value problem of fractional order on unbounded domains in a Banach space. Nonlinear Anal. 74, 2844-2852 (2011) MATH MathSciNet CrossRef
  14. Liang, S, Zhang, J: Existence of three positive solutions for m-point boundary value problems for some nonlinear fractional differential equations on an infinite interval. Comput. Math. Appl. 61, 3343-3354 (2011) MATH MathSciNet CrossRef
  15. Maagli, H: Existence of positive solutions for a nonlinear fractional differential equation. Electron. J. Differ. Equ. 2013, 29 (2013) MathSciNet CrossRef
  16. Su, X, Zhang, S: Unbounded solutions to a boundary value problem of fractional order on the half-line. Comput. Math. Appl. 61, 1079-1087 (2011) MATH MathSciNet CrossRef
  17. Zhang, X: Existence and iteration of positive solutions for high-order fractional differential equations with integral conditions on a half-line. J. Appl. Math. Comput. 45, 137-150 (2014) MATH MathSciNet CrossRef
  18. Arara, A, Benchohra, M, Hamidi, N, Nieto, JJ: Fractional order differential equations on an unbounded domain. Nonlinear Anal. 72, 580-586 (2010) MATH MathSciNet CrossRef
  19. Liang, S, Zhang, J: Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval. Math. Comput. Model. 54, 1334-1346 (2011) MATH MathSciNet CrossRef
  20. Lakoud, AG, Kcman, A: Unbounded solution for a fractional boundary value problem. Adv. Differ. Equ. 2014, 154 (2014) CrossRef
  21. Liang, S, Shi, S: Existence of multiple positive solutions for m-point fractional boundary value problems with p-Laplacian operator on infinite interval. J. Appl. Math. Comput. 38, 687-707 (2012) MATH MathSciNet CrossRef
  22. Wang, G, Liu, S, Zhang, L: Iterative approximation of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain. J. Funct. Spaces 2014, Article ID 469509 (2014) MathSciNet
  23. Yao, S, Wang, G, Li, Z, Yu, L: Positive solutions for three-point boundary value problem of fractional differential equation with p-Laplacian operator. Discrete Dyn. Nat. Soc. 2013, Article ID 376938 (2013) MathSciNet
  24. Jiang, M, Zhong, S: Successively iterative method for fractional differential equations with integral boundary conditions. Appl. Math. Lett. 38, 94-99 (2014) MathSciNet CrossRef
  25. Sun, Y, Zhao, M: Positive solutions for a class of fractional differential equations with integral boundary conditions. Appl. Math. Lett. 34, 17-21 (2014) MathSciNet CrossRef
  26. Corduneanu, C: Integral Equations and Stability of Feedback Systems. Academic Press, New York (1973) MATH
  27. Liu, YS: Boundary value problem for second order differential equations on unbounded domain. Acta Anal. Funct. Appl. 4, 211-216 (2002) MATH MathSciNet
  
• 作者单位：Bingxian Li (1)
  Shurong Sun (1)
  Zhenlai Han (1)
  
  1. School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, P.R. China
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

In this paper, we study the existence of the positive solutions for a class of high-order differential equations with multi-point boundary value conditions involving the Caputo fractional derivative on infinite interval. Moreover, we develop two computable explicit monotone iterative sequences for approximating the two minimal and maximal positive solutions. An example is given to show the applicability of our main results. Keywords Caputo fractional derivative multi-point boundary value problem monotone iteration method infinite interval existence of solutions