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Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance

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Abstract

In this paper, we consider the following two-point boundary value problem for fractional p-Laplace differential equation

where \(D^{\alpha}_{0^{+}}\), \(D^{\beta}_{0^{+}}\) denote the Caputo fractional derivatives, 0<α,β≤1, 1<α+β≤2. By using the coincidence degree theory, a new result on the existence of solutions for above fractional boundary value problem is obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is inserted to illustrate the validity and practicability of our main results.

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Acknowledgements

The author would like to thank the referee for his or her careful reading and some comments on improving the presentation of this paper.

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Authors and Affiliations

  1. College of Mathematics and Physics, Jinggangshan University, Ji’an, Jiangxi, 343009, P.R. China

    Xiaosong Tang & Changyuan Yan

  2. College of Electronics and Information Engineering, Jinggangshan University, Ji’an, Jiangxi, 343009, P.R. China

    Qing Liu

Authors
  1. Xiaosong Tang
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  2. Changyuan Yan
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  3. Qing Liu
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Corresponding author

Correspondence to Xiaosong Tang.

Additional information

Supported by the Youth NSF of Jiangxi Province (20114BAB211015), the Youth NSF of the Education Department of Jiangxi Province (GJJ11180), the NSF of Jinggangshan University.

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Tang, X., Yan, C. & Liu, Q. Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance. J. Appl. Math. Comput. 41, 119–131 (2013). https://doi.org/10.1007/s12190-012-0598-0

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  • DOI: https://doi.org/10.1007/s12190-012-0598-0

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