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Results on finite time stability of various fractional order systems

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  • Panda, Sumati Kumari
  • Vijayakumar, Velusamy

Abstract

This article deals with the existence of the solution of Hilfer–Katugampola fractional derivatives, and we prove the stability results of the equilibrium point of the presented problem. Numerous authors have made substantial use of the concepts of fractional derivatives and fixed-point theory in order to produce stability results in neural networks containing complex-valued or real-valued inputs. In this connection, we discuss the finite stability of Caputo fractional derivatives as well as Caputo fractional-order complex-valued neural networks. We provide a numerical result that supports the theoretical discussion.

Suggested Citation

  • Panda, Sumati Kumari & Vijayakumar, Velusamy, 2023. "Results on finite time stability of various fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s096007792300807x
    DOI: 10.1016/j.chaos.2023.113906
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    References listed on IDEAS

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    1. Panda, Sumati Kumari & Abdeljawad, Thabet & Ravichandran, C., 2020. "A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    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. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. J. A. Tenreiro Machado & Manuel F. Silva & Ramiro S. Barbosa & Isabel S. Jesus & Cecília M. Reis & Maria G. Marcos & Alexandra F. Galhano, 2010. "Some Applications of Fractional Calculus in Engineering," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-34, November.
    5. Abdon Atangana & Necdet Bildik, 2013. "The Use of Fractional Order Derivative to Predict the Groundwater Flow," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, October.
    6. Badr Alqahtani & Andreea Fulga & Erdal Karapınar & Panda Sumati Kumari, 2019. "Sehgal Type Contractions on Dislocated Spaces," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    7. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
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    Cited by:

    1. Jia, Wenwen & Xie, Jingu & Guo, Haihua & Wu, Yongbao, 2024. "Intermittent boundary control for fixed-time stability of reaction–diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Panda, Sumati Kumari & Vijayakumar, Velusamy & Nagy, A.M., 2023. "Complex-valued neural networks with time delays in the Lp sense: Numerical simulations and finite time stability," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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