Kyungpook Mathematical Journal

  • 제56권2호
  • /
  • Pages.419-430
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  • 2016
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation

  • Yang, Wengui (Ministry of Public Education, Sanmenxia Polytechnic)
  • 투고 : 2013.04.16
  • 심사 : 2016.04.11
  • 발행 : 2016.06.23
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초록

In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

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참고문헌

  1. R. P. Agarwal, Certain fractional q-integrals and q-derivatives, Proc. Cambridge Philos. Soc., 66(1969), 365-370. https://doi.org/10.1017/S0305004100045060
  2. R. P. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72(2010), 2859-2862. https://doi.org/10.1016/j.na.2009.11.029
  3. R. P. Agarwal, D. O'Regan, Svatoslav Stanek, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. Math. Anal. Appl., 371(2010), 57-68. https://doi.org/10.1016/j.jmaa.2010.04.034
  4. B. Ahmad, J. J. Nieto, J. Pimentel, Some boundary value problems of fractional differential equations and inclusions, Comput. Math. Appl., 62(2011), 1238-1250. https://doi.org/10.1016/j.camwa.2011.02.035
  5. F. M. Atici, P. W. Eloe, Fractional q-calculus on a time scale, J. Nonlinear Math. Phys., 14(2007), 333-344.
  6. W. A. Al-Salam, Some fractional q-integrals and q-derivatives, Proc. Edinb. Math. Soc., 15(2)(1966-1967), 135-140.
  7. Z. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal., 72 (2010), 916-924. https://doi.org/10.1016/j.na.2009.07.033
  8. M. El-Shahed, F. M. Al-Askar, Positive solutions for boundary value problem of nonlinear fractional q-difference equation, ISRN Math. Anal., 2011(2011), Art. ID 385459, 12 pages.
  9. M. El-Shahed, F. M. Al-Askar, On the existence and uniqueness of solutions for q-fractional boundary value problem, Int. J. Math. Anal., 5(2011), 1619-1630.
  10. M. El-Shahed, H. A. Hassan, Positive solutions of q-difference equation, Proc. Amer. Math. Soc.,
  11. R. A. C. Ferreira, Nontrivial solutions for fractional q-difference boundary value problems, Electron. J. Qual. Theory Differ. Equ., 70(2010), 1-10.
  12. R. A. C. Ferreira, Positive solutions for a class of boundary value problems with fractional q-differences, Comput. Math. Appl., 61(2011), 367-373. https://doi.org/10.1016/j.camwa.2010.11.012
  13. F. H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46(1908), 253-281.
  14. F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41(1910). 193-203.
  15. V. Kac and P. Cheung, Quantum Calculus, Springer, New York, NY, USA, 2002.
  16. C. Li, X. Luo, Y. Zhou, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Comput. Math. Appl., 59(2010), 1363-1375. https://doi.org/10.1016/j.camwa.2009.06.029
  17. P. M. Rajkovic, S. D. Marinkovic, and M. S. Stankovic, On q-analogues of caputo derivative and Mittag-Leer function, Fract. Calc. Appl. Anal., 10(2007), 359-373.
  18. P. M. Rajkovic, S. D. Marinkovic, and M. S. Stankovic, Fractional integrals and derivatives in q-calculus, Appl. Anal. Discrete Math., 1(2007), 311-323. https://doi.org/10.2298/AADM0701311R
  19. M. S. Stankovic, P. M. Rajkovic, and S.D. Marinkovic, On q-fractional derivatives of Riemann-Liouville and Caputo type, 2009, http://arxiv.org/abs/0909.0387.
  20. D. R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.

피인용 문헌

  1. Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions vol.4, pp.4, 2016, https://doi.org/10.3390/math4040063
  2. Properties of positive solutions for m-point fractional differential equations on an infinite interval pp.1579-1505, 2019, https://doi.org/10.1007/s13398-018-0548-2
  3. Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations vol.10, pp.9, 2018, https://doi.org/10.3390/sym10090358