Abstract
In this paper, a numerical method based on the Lagrangian piece-wise interpolation is proposed to solve variable-order fractal-fractional time delay equations with power law, exponential decay and Mittag-Leffler memories. These operators permit to describe physical phenomena with variable memory and fractal variable dimension. Numerical methods were applied to simulate the variable-order time delay Mackey–Glass and synaptically coupled FitzHugh–Nagumo models. Our numerical simulations display several new attractors.
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Acknowledgements
Jesús Emmanuel Solís Pérez acknowledges the support provided by CONACyT through the assignment doctoral fellowship. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.
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Solís-Pérez, J.E., Gómez-Aguilar, J.F. Variable-order fractal-fractional time delay equations with power, exponential and Mittag-Leffler laws and their numerical solutions. Engineering with Computers 38, 555–577 (2022). https://doi.org/10.1007/s00366-020-01065-0
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DOI: https://doi.org/10.1007/s00366-020-01065-0