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Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods

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  • Zhao, Yulin
  • Chen, Haibo
  • Qin, Bin

Abstract

In this paper, a coupled system of nonlinear fractional differential equations is considered. The existence of at least three distinct weak solutions is obtained by means of the variational methods and the critical point theory due to Bonanno and Marano. In addition, an example is presented to illustrate the feasibility and effectiveness of the main results.

Suggested Citation

  • Zhao, Yulin & Chen, Haibo & Qin, Bin, 2015. "Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 417-427.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:417-427
    DOI: 10.1016/j.amc.2014.12.128
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    References listed on IDEAS

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    1. Jia, Mei & Liu, Xiping, 2014. "Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 313-323.
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    Cited by:

    1. Fares Kamache & Rafik Guefaifia & Salah Boulaaras & Asma Alharbi, 2020. "Existence of Weak Solutions for a New Class of Fractional p -Laplacian Boundary Value Systems," Mathematics, MDPI, vol. 8(4), pages 1-18, March.
    2. Zhao, Yulin & Chen, Haibo & Xu, Chengjie, 2017. "Nontrivial solutions for impulsive fractional differential equations via Morse theory," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 170-179.
    3. Danyang Kang & Cuiling Liu & Xingyong Zhang, 2020. "Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p -Laplacian," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    4. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    5. Salari, Amjad & Ghanbari, Behzad, 2019. "Existence and multiplicity for some boundary value problems involving Caputo and Atangana–Baleanu fractional derivatives: A variational approach," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 312-317.
    6. Yulin Zhao & Jiafa Xu & Haibo Chen, 2019. "Variational Methods for an Impulsive Fractional Differential Equations with Derivative Term," Mathematics, MDPI, vol. 7(10), pages 1-15, September.
    7. Dongdong Gao & Jianli Li, 2021. "New results for impulsive fractional differential equations through variational methods," Mathematische Nachrichten, Wiley Blackwell, vol. 294(10), pages 1866-1878, October.

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