Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions

Meng Zhang; Qiuping Li

doi:doi:10.11648/j.ijtam.20170301.18

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Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions

Meng Zhang, Qiuping Li

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)

Received: 29 October 2016 Accepted: 6 January 2017 Published: 18 January 2017

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Abstract

In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion obtained results with others.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.ijtam.20170301.18
Page(s)	49-53
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Fractional Differential Equation, Boundary Value Problem, Nonlinear Nonlocal Boundary Condition, Positive Solution, Fractional Green's Function, Guo–Krasnosel’skii Fixed Point Theorem

References

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[2]	K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
[3]	I. Podlubny, Fractional Differential Equations, Academic Press, New York / Lindo n /Toronto, 1999.
[4]	S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integral and Derivative. Theory and Applications, Gordon and Breach, Switzerland, 1993.
[5]	D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996) 609–625.
[6]	Y. Zhao, S. Sun, Z. Han, Q. Li, Positive solutions to boundary value problems of nonlinear fractional differential equations, Abs. Appl. Anal. 2011 (2011) Article ID 390543, 1–16.
[7]	Jiang, W. Eigenvalue interval for multi-point boundary value problems of fractional differential equations. Appl. Math. Comput. 219 (2013)4570-4575.
[8]	Anguraj, A, Karthikeyan, P, Rivero, M, Trujillo, JJ, On new existence results for fractional integro-differential equations with impulsive and integral conditions. Comput. Math. Appl. 66 (2014), 2587-2594.
[9]	D. Jiang, C. Yuan, The positive properties of the Green function for Dirichlet type boundary value problems of nonlinear fractional differential equations and its application, Nonlinear Anal. TMA 72 (2010) 710-719.
[10]	Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005) 495–505.
[11]	S. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Electron. J. Differ. Equ. 36 (2006) 1–12.
[12]	Y. Zhao, S. Sun, Z. Han, Q. Li, The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations, Commun. Nonlinear Sci. Numer. Simul. 16 (2011) 2086–2097.
[13]	X. Xu, D. Jiang, C. Yuan, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Anal. 71 (2009) 4676–4688.
[14]	Y. Zhao, S. Sun, Z. Han, M. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Appl. Math. Comput. 217 (2011) 6950–6958.
[15]	S. Sun, Y. Zhao, Z. Han, J. liu, Eigenvalue problem for a class of nonlinear fractional differential equations, Ann. Funct. Anal. 4 (2013) 25C39.
[16]	Vong, S, Positive solutions of singular fractional differential equations with integral boundary conditions. Math. Comput. Model. 57 (2013) 1053-1059.
[17]	A. A. Kilbas, H. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam, 2006.
[18]	W. Feng, S. Sun, X. Li, M. Xu, Positive solutions to fractional boundary value problems with nonlinear boundary conditions. Boundary Value Problems 2014: 225, doi: 10.1186/s13661-014-0225-0.
[19]	M. A. Krasnoselskii, Positive solution of operator equation, Noordhoff Groningen, 1964.

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Meng Zhang, Qiuping Li. (2017). Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions. International Journal of Theoretical and Applied Mathematics, 3(1), 49-53. https://doi.org/10.11648/j.ijtam.20170301.18

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ACS Style

Meng Zhang; Qiuping Li. Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Int. J. Theor. Appl. Math. 2017, 3(1), 49-53. doi: 10.11648/j.ijtam.20170301.18

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AMA Style

Meng Zhang, Qiuping Li. Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Int J Theor Appl Math. 2017;3(1):49-53. doi: 10.11648/j.ijtam.20170301.18

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@article{10.11648/j.ijtam.20170301.18,
  author = {Meng Zhang and Qiuping Li},
  title = {Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {49-53},
  doi = {10.11648/j.ijtam.20170301.18},
  url = {https://doi.org/10.11648/j.ijtam.20170301.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.18},
  abstract = {In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion obtained results with others.},
 year = {2017}
}

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TY  - JOUR
T1  - Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions
AU  - Meng Zhang
AU  - Qiuping Li
Y1  - 2017/01/18
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170301.18
DO  - 10.11648/j.ijtam.20170301.18
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 49
EP  - 53
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170301.18
AB  - In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion obtained results with others.
VL  - 3
IS  - 1
ER  -

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Author Information

Meng Zhang

Department of Mathematics, University of Jinan Quancheng Colllege, Penglai, P R China
Qiuping Li

Department of Mathematics, University of Jinan Quancheng Colllege, Penglai, P R China

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APA Style

Meng Zhang, Qiuping Li. (2017). Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions. International Journal of Theoretical and Applied Mathematics, 3(1), 49-53. https://doi.org/10.11648/j.ijtam.20170301.18

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ACS Style

Meng Zhang; Qiuping Li. Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Int. J. Theor. Appl. Math. 2017, 3(1), 49-53. doi: 10.11648/j.ijtam.20170301.18

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AMA Style

Meng Zhang, Qiuping Li. Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Int J Theor Appl Math. 2017;3(1):49-53. doi: 10.11648/j.ijtam.20170301.18

Copy | Download

@article{10.11648/j.ijtam.20170301.18,
  author = {Meng Zhang and Qiuping Li},
  title = {Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {49-53},
  doi = {10.11648/j.ijtam.20170301.18},
  url = {https://doi.org/10.11648/j.ijtam.20170301.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.18},
  abstract = {In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion obtained results with others.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions
AU  - Meng Zhang
AU  - Qiuping Li
Y1  - 2017/01/18
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170301.18
DO  - 10.11648/j.ijtam.20170301.18
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 49
EP  - 53
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170301.18
AB  - In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion obtained results with others.
VL  - 3
IS  - 1
ER  -

Copy | Download