Mondal A, Upadhyay RK. (2018). Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking Nonlinear Dynamics. 91

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References and models cited by this paper

Anastasio TJ. (1994). The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biological cybernetics. 72 [PubMed]

Anastasio TJ. (1998). Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior. Biological cybernetics. 79 [PubMed]

Caputo M. (1967). Linear models of dissipation whose Q is almost frequency independent-II Geophys J Int. 13

Chen L, Wu R, Chai Y, Qu J, Qi G. (2013). Synchronization of a class of fractional-order chaotic neural networks Entropy. 15(8)

Cole KS. (1933). Electric conductance of biological systems In: Cold Spring Harbor Symposia On Quantitative Biology. 1

Connors BW, Gutnick MJ. (1990). Intrinsic firing patterns of diverse neocortical neurons. Trends in neurosciences. 13 [PubMed]

Dokoumetzidis A, Macheras P. (2009). Fractional kinetics in drug absorption and disposition processes. Journal of pharmacokinetics and pharmacodynamics. 36 [PubMed]

Drew PJ, Abbott LF. (2006). Models and properties of power-law adaptation in neural systems. Journal of neurophysiology. 96 [PubMed]

Goychuk I, Hänggi P. (2004). Fractional diffusion modeling of ion channel gating. Physical review. E, Statistical, nonlinear, and soft matter physics. 70 [PubMed]

Gray CM, McCormick DA. (1996). Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science (New York, N.Y.). 274 [PubMed]

Hsu I, Kazarinoc NK. (1976). An applicable Hopf bifurcation formula and stability of small periodic solutions of the Field-Noyes Model. J Math Anal Appl. 55

Hsü ID, Kazarinoff ND. (1977). Existence and stability of periodic solutions of a third-order non-linear autonomous system simulating immune response in animals Proc R Soc Edinb. 77A

Izhikevich EM. (2000). Neural excitability, spiking and bursting Int J Bifurcat Chaos Appl Sci Eng. 10

Izhikevich EM. (2003). Simple model of spiking neurons. IEEE transactions on neural networks. 14 [PubMed]

Izhikevich EM. (2004). Which model to use for cortical spiking neurons? IEEE transactions on neural networks. 15 [PubMed]

Jun D, Guang-Jun Z, Yong X, Hong Y, Jue W. (2014). Dynamic behavior analysis of fractional-order Hindmarsh-Rose neuronal model. Cognitive neurodynamics. 8 [PubMed]

Kaslik E, Sivasundaram S. (2012). Nonlinear dynamics and chaos in fractional-order neural networks. Neural networks : the official journal of the International Neural Network Society. 32 [PubMed]

Kistler WM, Gerstner W. (2002). Spiking neuron models.

Koch C, Adams PR, Yamada WM. (1989). Multiple channels and calcium dynamics Methods In Neuronal Modeling: From Synapses To Networks.

Kopell N, Ermentrout GB. (1986). Parabolic bursting in an excitable system coupled with a slow oscillation. Siam J Appl Math. 46

La Camera G et al. (2006). Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons. Journal of neurophysiology. 96 [PubMed]

Lewen GD et al. (2001). Multiple timescales of adaptation in a neural code Advances In Neural Information Processing Systems. 13

Li C, Chen Y, Kurths J. (2013). Fractional calculus and its applications. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. 371 [PubMed]

Lundstrom BN, Higgs MH, Spain WJ, Fairhall AL. (2008). Fractional differentiation by neocortical pyramidal neurons. Nature neuroscience. 11 [PubMed]

Ma J, Lv M. (2016). Multiple modes of electrical activities in a new neuron model under electromagnetic radiation Neurocomputing. 205

Ma J, Wang C, Song X, Lv M, Ren G. (2016). Model of electrical activity in a neuron under magnetic flow effect Nonlinear Dyn. 85(3)

Magin R. (2010). Fractional calculus models of complex dynamics in biological tissues Computers Mathematics With Applications. 59

Magin RL. (2004). Fractional calculus in bioengineering. Critical reviews in biomedical engineering. 32 [PubMed]

Magin RL, Hanyga A. (2014). A new anisotropic fractional model of diffusion suitable for applications of diffusion tensor imaging in biological tissues Proc R Soc A. 470

Magin RL, Ovadia M. (2008). Modeling the cardiac tissue electrode interface using fractional calculus J Vib Control. 14

Miller KD, Troyer TW. (2002). Neural noise can explain expansive, power-law nonlinearities in neural response functions. Journal of neurophysiology. 87 [PubMed]

Moaddy K, Radwan A, Salama K, Momani S, Hashim I. (2012). The fractionalorder modeling and synchronization of electrically coupled neuron systems Computers Mathematics With Applications. 64

Momani S, Odibat Z. (2007). Numerical comparison of methods for solving linear differential equations of fractional order Chaos Solitons Fract. 31

Mondal A, Upadhyay RK. (2015). Dynamics of fractional order modified Morris-Lecar neural model Netw Biol. 5

Mondal A, Upadhyay RK, Teka WW. (2017). Fractional order excitable neural system with bidirectional coupling Nonlinear Dyn. 87

Nagy A, Sweilam N. (2014). An efficient method for solving fractional Hodgkin–Huxley model Physics Letters A. 378(30)

Oldham KB, Spanier J. (1974). The fractional calculus. 17

Paulin MG, Hoffman LF, Assad C. (2004). Dynamics and the single spike. IEEE transactions on neural networks. 15 [PubMed]

Petráš I, Magin RL. (2011). Simulation of Drug Uptake in a Two Compartmental Fractional Model for a Biological System. Communications in nonlinear science & numerical simulation. 16 [PubMed]

Podlubny I. (1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications.

Podlubny I. (2002). Geometric and physical interpretation of fractional integration and fractional differentiation Fract Calculus Appl Anal. 5

Podlubny I et al. (2015). Diffusion process modeling by using fractional-order models Appl Math Comput. 257

Radwan A, Armanyos M. (2016). Fractional-order FitzhughNagumo and Izhikevich neuron models 13Th International Conference On Electrical Engineering/Electronics.

Ross B, Miller KS. (1993). An introduction to the fractional calculus and fractional differential equations.

Safdari H et al. (2016). Fractional Dynamics of Network Growth Constrained by Aging Node Interactions. PloS one. 11 [PubMed]

Santamaria F, Teka W, Stockton D. (2016). Power-law dynamics of membrane conductances increase spiking diversity in a Hodgkin-Huxley model PLoS Comput Biol. 12(3)

Sherief H, El-Sayed AMA, Behiry SH, Raslan WE. (2012). Using Fractional Derivatives to Generalize the Hodgkin– Huxley Model Fractional Dynamics and Control.

Tang Y, Huang J, Scherer R, Kalla SL. (2011). The GrunwaldLetnikov method for fractional differential equations Comput Math Appl. 62

Teka W, Marinov TM, Santamaria F. (2014). Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model. PLoS computational biology. 10 [PubMed]

Teka W, Tabak J, Vo T, Wechselberger M, Bertram R. (2011). The dynamics underlying pseudo-plateau bursting in a pituitary cell model. Journal of mathematical neuroscience. 1 [PubMed]

Teka WW, Upadhyay RK, Mondal A. (2017). Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics. Neural networks : the official journal of the International Neural Network Society. 93 [PubMed]

Ulanovsky N, Las L, Farkas D, Nelken I. (2004). Multiple time scales of adaptation in auditory cortex neurons. The Journal of neuroscience : the official journal of the Society for Neuroscience. 24 [PubMed]

Wang Y, Wu F, Xu Y, Ma J, Zhou P. (2017). The electrical activity of neurons subject to electromagnetic induction and Gaussian white noise Int J Bifurc Chaos. 27

Wang Z, Shi M. (2014). Abundant bursting patterns of a fractional-order Morris-Lecar neuron model Commun Nonlinear Sci Numer Simul. 19

Weinberg SH. (2015). Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model. PloS one. 10 [PubMed]

Westerlund S, Ekstam L. (1994). Capacitor theory IEEE Trans Dielectr Electr Insul. 1(8)

Xu J, Ma J. (2015). An introduction and guidance for neurodynamics Sci Bull. 60

Zhou Y, Ionescu C, Tenreiro Machado JA. (2015). Fractional dynamics and its applications Nonlinear Dyn. 80

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