References
- G. Long, G. Fang, “A review of biologically plausible neuron models for spiking neural networks.” AIAA Infotech@ Aerospace 2010, vol. 3540, 2010.
- W. Gerstner, R. Naud, “How good are neuron models?” Science, vol.326, no.5951, p.p. 379-380, 2009.
- R. FitzHugh, “Impulses and physiological states in theoretical models of nerve membrane”, Biophysical journal, vol. 1, no. 6, pp. 445-466, 1961.
- J. Nagumo, S. Arimoto, and S. Yoshizawa. “An active pulse transmission line simulating nerve axon.” Proceedings of the IRE vol. 50, no.10, pp. 2061-2070, 1962.
- A. L. Hodgkin, and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve.” The Journal of physiology, vol. 117, no. 4, pp. 500-544, 1952.
- E. Izhikevich, “Simple Model of Spiking Neurons,” IEEE Transactions on Neural Networks, vol. 14, no. 6, pp. 1569-1572, 2003.
- Simple Model of Spiking Neurons, [Online]. Available: https://www.izhikevich.org/publications/spikes.htm (Access Date: 28/12/2021).
- L. F. Abbott, “Lapicque’s introduction of the integrate-and-fire model neuron (1907)” Brain research bulletin, vol. 50, no. 5-6, pp. 303-304, 1999.
- M. J. Richardson, N. Brunel, and V. Hakim, “From subthreshold to firing-rate resonance.” Journal of neurophysiology vol. 89, no.5, pp. 2538-2554, 2003.
- T. Wondimu, T. M. Marinov, and F. Santamaria, “Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model.” PLoS computational biology vol. 10, no.3, pp. e1003526, 2014.
- W. Gerstner, W. M. Kistler, R. Naud, and L. Paninski, Neuronal dynamics: From single neurons to networks and models of cognition, Cambridge University Press, 2014.
- K. G. Pearson, “Neural adaptation in the generation of rhythmic behavior.” Annual review of physiology, vol. 62, no.1, pp. 723-753, 2000.
- S. Chung, X. Li, and S. B. Nelson, “Short-term depression at thalamocortical synapses contributes to rapid adaptation of cortical sensory responses in vivo.” Neuron, vol.34, no.3, pp. 437-446, 2002.
- D. Valério, J. Machado, and V. Kiryakova, “Some pioneers of the applications of fractional calculus”, Fract. Calc. Appl. Anal., vol.17, no.2, pp.552–578, 2014.
- S.M. Shah, R. Samar, N. M. Khan, and M. A. Z. Raja, “Fractional-order adaptive signal processing strategies for active noise control systems.” Nonlinear Dynamics, Vol. 85, pp. 1363–1376, 2016.
- D. del-Castillo-Negrete, B. A. Carreras, and V. E. Lynch, “Fractional diffusion in plasma turbulence.” Physics of Plasmas, vol. 11, no. 8, pp. 3854-3864, 2004.
- V.E. Tarasov, “Review of some promising fractional physical models.” International Journal of Modern Physics B, vol. 27, no.09, pp. 1330005, 2013.
- M. Caputo, “Linear Models of Dissipation whose Q is almost Frequency Independent II”, Geophysical Journal International, vol. 13, no. 5, pp. 529–539, 1967.
- R. Agarwal, M. Belmekki, and M. Benchohra. “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative.” Advances in Difference Equations, vol. 2009, pp. 1-47, 2009.
- R. Scherer, S. L. Kalla, Y. Tang, and J. Huang, “The Grünwald–Letnikov method for fractional differential equations.” Computers & Mathematics with Applications, vol. 62, no.3, pp. 902-917, 2011.
- R. Khalil, M. A. Horani, A. Yousef, and M. Sababheh, “A new definition of fractional derivative.” Journal of computational and applied mathematics, vol. 264, pp. 65–70, 2014.
- T. Abdeljawad, T. “On conformable fractional calculus.” Journal of computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.
- A. O. Akdemir, H. Dutta, and A. Atangana, eds. Fractional order analysis: theory, methods and applications. John Wiley & Sons, 2020.
- R. Sikora, R. “Fractional derivatives in electrical circuit theory–critical remarks.” Archives of Electrical Engineering, vol. 66, no. 1, pp. 155-163, 2017.
- T. J. Anastasio, “The fractional-order dynamics of brainstem vestibulo-oculomotor neurons.” Biological cybernetics, vol. 72, no. 1, pp. 69-79, 1994.
- K. Moaddy, A. G. Radwan, K. N. Salama, S. Momani, and I. Hashim, “The fractional-order modeling and synchronization of electrically coupled neuron systems.” Computers & Mathematics with Applications, vol. 64, no.10, pp. 3329-3339, 2012.
- M. Yavuz, B. Yaşkıran, “Conformable Derivative Operator in Modelling Neuronal Dynamics.” Applications & Applied Mathematics, vol. 13, no.2, 2018.
- M. Armanyos, A. G. Radwan. “Fractional-order Fitzhugh-Nagumo and Izhikevich neuron models.” 2016 13th international conference on electrical engineering/electronics, computer, telecommunications and information technology (ECTI-CON), pp. 1-5, 2016.
- L. Martínez, J. J. Rosales, C. A. Carreño, and J. M. Lozano, “Electrical circuits described by fractional conformable derivative.” International Journal of Circuit Theory and Applications, vol. 46, no.5, pp. 1091-1100, 2018.
- U. Palaz, R. Mutlu, “Analysis of a Capacitor Modelled with Conformable Fractional Derivative Under DC and Sinusoidal Signals.” Celal Bayar University Journal of Science, vol. 17, no. 2, p. p. 193-198, 2021.
- A. Petrovas, S. Lisauskas, and A. Slepikas. “Electronic model of fitzhugh-nagumo neuron.” Elektronika Ir Elektrotechnika, vol. 122, no .6, pp. 117-120, 2012.
- M. Chen, J. Qi, Q. Xu, and B. Bao, “Quasi-period, periodic bursting and bifurcations in memristor-based FitzHugh-Nagumo circuit.” AEU-International Journal of Electronics and Communications, vol. 110, pp. 152840, 2019.
- E. M. Izhikevich, R. FitzHugh, “FitzHugh-nagumo model.” Scholarpedia, vol. 1, no. 9, p. p. 1349, 2006.
- T. Kanamaru, “Van der Pol oscillator.” Scholarpedia vol. 2, no. 1 pp. 2202, 2007.