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A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations

Author

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  • Zúñiga-Aguilar, C.J.
  • Gómez-Aguilar, J.F.
  • Escobar-Jiménez, R.F.
  • Romero-Ugalde, H.M.

Abstract

In this work, we present a novel numerical method based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation to solve numerically fractional delay differential equations. We focus on the fractional derivative with power-law, exponential decay and Mittag-Leffler kernel of Liouville-Caputo type with constant and variable-order. The numerical methods were applied to simulate the Duffing attractor, El-Niño/Southern-Oscillation, and Ikeda systems.

Suggested Citation

  • Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:266-282
    DOI: 10.1016/j.chaos.2019.06.009
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    Cited by:

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    2. Panj-Mini, H. & Parsa Moghaddam, B. & Hashemizadeh, E., 2021. "A class of computational approaches for simulating fractional functional differential equations via Dickson polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Chen, Yun & Xu, Yanyi & Lin, Qian & Zhang, Xiyong, 2020. "Model and criteria on the global finite-time synchronization of the chaotic gyrostat systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 515-533.
    4. Jaradat, Imad & Alquran, Marwan & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2022. "Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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