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Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation

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

Abstract

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

참고문헌 (20)

  1. R. P. Agarwal, "Certain fractional q-integrals and q-derivatives", Proc. Cambridge Philos. Soc., 66, pp.365~370 (1969)
  2. R. P. Agarwal, "On the concept of solution for frac-tional differential equations with uncertainty", Nonlinear Anal., 72, pp.2859~2862 (2010)
  3. R. P. Agarwal, "Svatoslav Stanek, Positive solutions for Dirichlet prob-lems of singular nonlinear fractional differential equations", J. Math. Anal. Appl., 371, pp.57~68 (2010)
  4. B. Ahmad, "Some boundary value problems of fractional differential equations and inclusions", Comput. Math. Appl., 62, pp.1238~1250 (2011)
  5. F. M. Atici, "Fractional q-calculus on a time scale", J. Nonlinear Math. Phys., 14, pp.333~344 (2007)
  6. W. A. Al-Salam, "Some fractional q-integrals and q-derivatives", Proc. Edinb. Math. Soc., 15(2), pp.135~140 (1966)
  7. Z. Bai, "On positive solutions of a nonlocal fractional boundary value problem", Nonlinear Anal., 72, pp.916~924 (2010)
  8. M. El-Shahed, "Positive solutions for boundary value problem of nonlinear fractional q-difference equation", ISRN Math. Anal., pp.385459~ (2011)
  9. M. El-Shahed, "On the existence and uniqueness of solutions for q-fractional boundary value problem", Int. J. Math. Anal., 5, pp.1619~1630 (2011)
  10. M. El-Shahed, "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, pp.1~10 (2010)
  12. R. A. C. Ferreira, "Positive solutions for a class of boundary value problems with fractional q-differences", Comput. Math. Appl., 61, pp.367~373 (2011)
  13. F. H. Jackson, "On q-functions and a certain difference operator", Trans. Roy. Soc. Edinburgh, 46, pp.253~281 (1908)
  14. F. H. Jackson, "On q-definite integrals", Quart. J. Pure Appl. Math., 41, pp.193~203 (1910)
  15. V. Kac, "Quantum Calculus" (2002), Springer
  16. C. Li, "Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations", Comput. Math. Appl., 59, pp.1363~1375 (2010)
  17. P. M. Rajkovic, "On q-analogues of caputo derivative and Mittag-Leer function", Fract. Calc. Appl. Anal., 10, pp.359~373 (2007)
  18. P. M. Rajkovic, "Fractional integrals and derivatives in q-calculus", Appl. Anal. Discrete Math., 1, pp.311~323 (2007)
  19. "On q-fractional derivatives of Riemann-Liouville and Caputo type" (2009)[URL]
  20. D. R. Smart, "Fixed Point Theorems" (1980), Cambridge University Press

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