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Analyzing the stability of fractal delay differential equations

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  • Khalili Golmankhaneh, Alireza
  • Tunç, Cemil

Abstract

In this paper, we provide a comprehensive overview of fractal calculus and investigate the stability of both linear and non-linear fractal delay differential equations with fractal support. Our analysis encompasses the stability of the fractal Mackey–Glass equation as well as fractal differential equations with single and dual delays. Additionally, we introduce a predictor–corrector scheme to solve the fractal one-delay differential equation. Several examples are presented to illustrate the effects of fractal-order differentiation, which arise from the dimensionality of the fractal support, and the impact of fractal delays.

Suggested Citation

  • Khalili Golmankhaneh, Alireza & Tunç, Cemil, 2024. "Analyzing the stability of fractal delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010440
    DOI: 10.1016/j.chaos.2024.115492
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    References listed on IDEAS

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    1. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.
    2. Khalili Golmankhaneh, Alireza & Ontiveros, Lilián Aurora Ochoa, 2023. "Fractal calculus approach to diffusion on fractal combs," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Khalili Golmankhaneh, Alireza & Tejado, Inés & Sevli, Hamdullah & Valdés, Juan E. Nápoles, 2023. "On initial value problems of fractal delay equations," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    4. Kang-Le Wang, 2024. "An Efficient Scheme For Two Different Types Of Fractional Evolution Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-11.
    5. Khalili Golmankhaneh, Alireza & Bongiorno, Donatella, 2024. "Exact solutions of some fractal differential equations," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    6. Alireza Khalili Golmankhaneh & Renat Timergalievich Sibatov, 2021. "Fractal Stochastic Processes on Thin Cantor-Like Sets," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    7. Emile F. Doungmo Goufo & Y. Khan & I. Tchangou Toudjeu, 2022. "The Fractal And Piecewise Structure Of Some Chaotic Neural Networks Using A Generalized Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-19, December.
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