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On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

Author

Listed:
  • Fares Kamache
  • Salah Mahmoud Boulaaras
  • Rafik Guefaifia
  • Nguyen Thanh Chung
  • Bahri Belkacem Cherif
  • Mohamed Abdalla

Abstract

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann‐Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ3 and ℝ4 are given to illustrate the theoritical results.

Suggested Citation

  • Fares Kamache & Salah Mahmoud Boulaaras & Rafik Guefaifia & Nguyen Thanh Chung & Bahri Belkacem Cherif & Mohamed Abdalla, 2021. "On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:5544740
    DOI: 10.1155/2021/5544740
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    References listed on IDEAS

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    1. Gao, Wei & Veeresha, P. & Prakasha, D.G. & Baskonus, Haci Mehmet & Yel, Gulnur, 2020. "New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. 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.
    3. Saima Rashid & Fahd Jarad & Muhammad Aslam Noor & Humaira Kalsoom & Yu-Ming Chu, 2019. "Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function," Mathematics, MDPI, vol. 7(12), pages 1-18, December.
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