Title: On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems
Author(s): B.M.B. Krushna, K.R. Prasad
Pages: 80-86
Cite as:
B.M.B. Krushna, K.R. Prasad, On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems, Int. J. Anal. Appl., 12 (2) (2016), 80-86.

Abstract


In this paper, we establish the existence of solutions to the fractional order three-point boundary value problems by utilizing Banach contraction principle and Schaefer's fixed point theorem.

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References


  1. Z. Bai and Y. Zhang, Solvability of fractional three-point boundary value problems with nonlinear growth, Appl. Math. Comput., 218(2011), 1719–1725. Google Scholar

  2. M. Benchohra, J. Henderson, S. K. Ntoyuas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), 1340–1350. Google Scholar

  3. M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Anal. TMA., 71(2009), 2391–2396. Google Scholar

  4. M. Feng, X. Zhang and W. Ge, New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions, Bound. Value Probl., 2011(2011), Article ID 720702. Google Scholar

  5. A. A. Kilbas and J. J. Trujillo, Differential equations of fractional order methods, results, problems, Appl. Anal., 78(2001), 153–192. Google Scholar

  6. A. A. Kilbas, H. M. Srivasthava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science, Amsterdam, 2006. Google Scholar

  7. R. A. Khan, M. Rehman and J. Henderson, Existence and uniqueness of solutions for nonlinear fractional differential equations with integral boundary conditions, Fract. Differ. Calc., 1(2011), 29–43. Google Scholar

  8. R. A. Khan and H. Khan, Existence of solution for a three-point boundary value problem of fractional differential equation, Journal of Fractional Calculus and Applications, 5(2014), 156–164. Google Scholar

  9. K. S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, 1993. Google Scholar

  10. Z. Ouyang and G. Li, Existence of the solutions for a class of nonlinear fractional order three-point boundary value problems with resonance, Bound. Value Probl., 2012(2012), Article ID 68, 1–13. Google Scholar

  11. I. Podulbny, Fractional Diffrential Equations, Academic Press, San Diego, 1999. Google Scholar

  12. K. R. Prasad and B. M. B. Krushna, Multiple positive solutions for a coupled system of Riemann–Liouville fractional order two-point boundary value problems, Nonlinear Stud., 20(2013), 501–511. Google Scholar

  13. K. R. Prasad and B. M. B. Krushna, Eigenvalues for iterative systems of Sturm–Liouville fractional order two-point boundary value problems, Fract. Calc. Appl. Anal., 17(2014), 638–653. Google Scholar

  14. K. R. Prasad and B. M. B. Krushna, Existence of solutions for a coupled system of three-point fractional order boundary value problems, Differ. Equ. Appl., 7(2015), 187–200. Google Scholar

  15. M. Rehman and R. A. Khan, Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations, Appl. Math. Lett., 23 (2010), 1038–1044. Google Scholar

  16. M. Rehman, R. A. Khan and N. A. Asif, Three point boundary value problems for nonlinear fractional differential equations, Acta Mathematica Scientia, 31(2011), 1337–1346. Google Scholar

  17. A. Shi and S. Zhang, Upper and lower solutions method and a fractional differential equation boundary value problem, Electron. J. Qual. Theory Differ. Equ., 30(2009), 1–13. Google Scholar

  18. G. Wang, S. K. Ntouyas and L. Zhang, Positive solutions of the three-point boundary value problem for fractional order differential equations with an advanced argument, Advances in Difference Equations, 2011(2011), Article ID 2. Google Scholar

  19. J. R. Wang, L. Lv and W. Wei, Differential equations of fractional order α ∈ (2,3) with boundary value conditions in abstract Banach spaces, Math. Commun., 17(2012), 371–387. Google Scholar

  20. S. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Electron. J. Differential Equations, 36(2006), 1–12. Google Scholar


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