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On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions

Author

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  • Rezapour, Sh.
  • Kumar, S.
  • Iqbal, M.Q.
  • Hussain, A.
  • Etemad, S.

Abstract

In this research, we investigate some conditions on the existence of solutions for two abstract multi-term sequential boundary value problems defined with the help of the Caputo derivatives. To do this, we consider some hypotheses on the existing single-valued and multi-valued functions defined in the given fractional differential equation and inclusion. In fact, according to the conditions of two versions of the Krasnoselskii’s fixed point theorems, we prove our required criteria which confirm the existence of solutions for the suggested boundary value problems. Finally, we consider some examples to show the consistency of our results numerically.

Suggested Citation

  • Rezapour, Sh. & Kumar, S. & Iqbal, M.Q. & Hussain, A. & Etemad, S., 2022. "On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 365-382.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:365-382
    DOI: 10.1016/j.matcom.2021.11.018
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    References listed on IDEAS

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    1. Shuman Meng & Yujun Cui, 2018. "The Uniqueness Theorem of the Solution for a Class of Differential Systems with Coupled Integral Boundary Conditions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-7, July.
    2. Dongxia Zan & Run Xu, 2018. "The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-8, October.
    3. Thongchai Dumrongpokaphan & Nichaphat Patanarapeelert & Thanin Sitthiwirattham, 2020. "On Sequential Fractional q -Hahn Integrodifference Equations," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    4. Kosmatov, Nickolai & Jiang, Weihua, 2016. "Resonant functional problems of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 573-579.
    5. Lu, Changna & Fu, Chen & Yang, Hongwei, 2018. "Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 104-116.
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    Cited by:

    1. Ahmed Salem & Rawia Babusail, 2022. "Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type," Mathematics, MDPI, vol. 10(9), pages 1-14, May.

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