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Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions

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  • Ahmad, Bashir
  • Luca, Rodica

Abstract

We investigate the existence of solutions for Caputo type sequential fractional integro-differential equations and inclusions subject to nonlocal boundary conditions involving Riemann–Liouville and Riemann–Stieltjes integrals. For the proofs of our main theorems we use the contraction mapping principle and the Krasnosel’skii fixed point theorem for the sum of two operators in the case of fractional equations, and the nonlinear alternative of Leray–Schauder type for Kakutani maps and the Covitz–Nadler fixed point theorem in the case of fractional inclusions. Some examples are presented to illustrate our results.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:516-534
    DOI: 10.1016/j.amc.2018.07.025
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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. Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. Wei Zhang & Wenbin Liu, 2020. "Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance," Mathematics, MDPI, vol. 8(1), pages 1-22, January.
    2. Ahmed Alsaedi & Amjad F. Albideewi & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    3. Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    4. Bashir Ahmad & Ymnah Alruwaily & Ahmed Alsaedi & Sotiris K. Ntouyas, 2019. "Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    5. Johnny Henderson & Rodica Luca & Alexandru Tudorache, 2021. "Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives," Mathematics, MDPI, vol. 9(7), pages 1-22, April.
    6. 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.
    7. Shahram Rezapour & Sotiris K. Ntouyas & Abdelkader Amara & Sina Etemad & Jessada Tariboon, 2021. "Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    8. Bashir Ahmad & Abrar Broom & Ahmed Alsaedi & Sotiris K. Ntouyas, 2020. "Nonlinear Integro-Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals with Nonlocal Boundary Data," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    9. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.

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