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A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

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  • Abbas, Saïd
  • Benchohra, Mouffak
  • Lazreg, Jamal-Eddine
  • Zhou, Yong

Abstract

In the present survey paper, we prove some results concerning the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations. Some attractivity and Ulam stability results are presented. Our results are provided by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.

Suggested Citation

  • Abbas, Saïd & Benchohra, Mouffak & Lazreg, Jamal-Eddine & Zhou, Yong, 2017. "A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 47-71.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:47-71
    DOI: 10.1016/j.chaos.2017.03.010
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    References listed on IDEAS

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    1. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    2. M. D. Qassim & K. M. Furati & N.-E. Tatar, 2012. "On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, June.
    3. Phollakrit Thiramanus & Sotiris K. Ntouyas & Jessada Tariboon, 2014. "Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, June.
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    Cited by:

    1. Cai, Ruiyang & Ge, Fudong & Chen, YangQuan & Kou, Chunhai, 2019. "Regional observability for Hadamard-Caputo time fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 190-202.
    2. B. Radhakrishnan & T. Sathya, 2022. "Controllability of Hilfer Fractional Langevin Dynamical System with Impulse in an Abstract Weighted Space," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 265-281, October.
    3. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Jiqiang Jiang & Donal O’Regan & Jiafa Xu & Yujun Cui, 2019. "Positive Solutions for a Hadamard Fractional p -Laplacian Three-Point Boundary Value Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    5. Saïd Abbas & Nassir Al Arifi & Mouffak Benchohra & Yong Zhou, 2019. "Random Coupled Hilfer and Hadamard Fractional Differential Systems in Generalized Banach Spaces," Mathematics, MDPI, vol. 7(3), pages 1-15, March.
    6. Ben Makhlouf, Abdellatif & Mchiri, Lassaad, 2022. "Some results on the study of Caputo–Hadamard fractional stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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