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On initial value problems of fractal delay equations

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  • Khalili Golmankhaneh, Alireza
  • Tejado, Inés
  • Sevli, Hamdullah
  • Valdés, Juan E. Nápoles

Abstract

In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phenomena with fractal time and fractal structure. Fractal retarded, neutral, and renewal delay differential equations with constant coefficients are solved by the method of steps and using Laplace transform. The graphs of solutions are given to show the details.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323001492
    DOI: 10.1016/j.amc.2023.127980
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    References listed on IDEAS

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    1. Wang, Yupin & Li, Xiaodi & Wang, Da & Liu, Shutang, 2022. "A brief note on fractal dynamics of fractional Mandelbrot sets," Applied Mathematics and Computation, Elsevier, vol. 432(C).
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    5. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.
    6. Zhou, Shengfan & Tian, Yongxiao & Wang, Zhaojuan, 2016. "Fractal dimension of random attractors for stochastic non-autonomous reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 80-95.
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    8. Huzak, Renato & Vlah, Domagoj & Žubrinić, Darko & Županović, Vesna, 2023. "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    9. Xu, Changjin & Farman, Muhammad & Akgül, Ali & Nisar, Kottakkaran Sooppy & Ahmad, Aqeel, 2022. "Modeling and analysis fractal order cancer model with effects of chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
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