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Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions

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  • Ahmad, Bashir
  • Luca, Rodica

Abstract

We investigate the existence and uniqueness of solutions for a system of nonlinear Caputo type sequential fractional integro-differential equations with coupled Riemann–Stieltjes integral boundary conditions, by using the Leray–Schauder alternative and the Banach contraction principle. Two examples are also presented to illustrate our results.

Suggested Citation

  • Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:378-388
    DOI: 10.1016/j.chaos.2017.08.035
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    References listed on IDEAS

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    1. Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    2. 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.
    3. J. Caballero & I. Cabrera & K. Sadarangani, 2012. "Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, October.
    4. Ahmad, Bashir & K. Ntouyas, Sotiris, 2015. "Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 615-622.
    5. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
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    Cited by:

    1. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    2. Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
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    4. Ahmed Alsaedi & Rodica Luca & Bashir Ahmad, 2020. "Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p -Laplacian Operators," Mathematics, MDPI, vol. 8(11), pages 1-18, October.

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