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406 Mathematical Techniques of Fractional Order Systems

Ismail, S.M., Said, L.A., Radwan, A.G., Madian, A.H., Abu-ElYazeed, M.F., Soliman, A.M.,
2015. Generalized fractional logistic map suitable for data encryption. 2015 International
Conference on Science and Technology (TICST). IEEE, pp. 336 341.
Ismail, S.M., Said, L.A., Rezk, A.A., Radwan, A.G., Madian, A.H., Abu-ElYazeed, M.F., et al.,
2017a. Biomedical image encryption based on double-humped and fractional logistic maps.
2017 6th International Conference on Modern Circuits and Systems Technologies
(MOCAST). IEEE, pp. 1 4.
Ismail, S.M., Said, L.A., Rezk, A.A., Radwan, A.G., Madian, A.H., Abu-Elyazeed, M.F., et al.,
2017b. Generalized fractional logistic map encryption system based on FPGA. {AEU}. Int.
J. Electr. Commun. 78, 1 27. Available from: https://doi.org/10.1016/j.aeue.2017.05.010.
URL: http://www.sciencedirect.com/science/article/pii/S143484111730376X.
Ismail, S.M., Said, L.A., Rezk, A.A., Radwan, A.G., Madian, A.H., Abu-ElYazeed, M.F., et al.,
2017c. Image encryption based on double-humped and delayed logistic maps for biomedical
applications. 2017 6th International Conference on Modern Circuits and Systems
Technologies (MOCAST). IEEE, pp. 1 4.
Jia, H.Y., Chen, Z.Q., Qi, G.Y., 2013. Topological horseshoe analysis and circuit realization for
a fractional-order Lu ¨ system. Nonlinear Dynam. 74, 203 212.
Levinsohn, E.A., Mendoza, S.A., Peacock-Lo ´pez, E., 2012. Switching induced complex dynam-
ics in an extended logistic map. Chaos Solitons Fractals 45, 426 432.
Lorenz, E.N., 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130 141.
Lu ¨, J., Chen, G., Cheng, D., Celikovsky, S., 2002. Bridge the gap between the Lorenz system
and the Chen system. Int. J. Bifurcation Chaos 12, 2917 2926.
Lu, J.G., Chen, G., 2006. A note on the fractional-order chen system. Chaos Solitons Fractals
27, 685 688.
Luo, Y., Chen, Y., 2012. Fractional order motion controls. John Wiley & Sons, Chichester.
Malek, K., Gobal, F., 2000. Application of chaotic logistic map for the interpretation of anion-
insertion in poly-ortho-aminophenol films. Synth. Metals 113, 167 171. Available from:
https://doi.org/10.1016/s0379-6779(00)00194-6. URL: https://doi.org/10.1016%2Fs0379-
6779%2800%2900194-6.
Matthews, R., 1989. On the derivation of a “chaotic” encryption algorithm. Cryptologia 13,
29 42.
Moaddy, K., Radwan, A.G., Salama, K.N., Momani, S., Hashim, I., 2012. The fractional-order
modeling and synchronization of electrically coupled neuron systems. Comput. Math.
Applicat. 64, 3329 3339.
Nejati, H., Beirami, A., Massoud, Y., 2008. A realizable modified tent map for true random
number generation. 51st Midwest Symposium on Circuits and Systems MWSCAS. IEEE,
pp. 621 624.
Ouannas, A., Azar, A.T., Ziar, T., Radwan, A.G., 2017a. Generalized synchronization of differ-
ent dimensional integer-order and fractional order chaotic systems. Fractional Order Control
and Synchronization of Chaotic Systems. Springer, pp. 671 697.
Ouannas, A., Azar, A.T., Ziar, T., Radwan, A.G., 2017b. A study on coexistence of different
types of synchronization between different dimensional fractional chaotic systems.
Fractional Order Control and Synchronization of Chaotic Systems. Springer, pp. 637 669.
Ouannas, A., Grassi, G., Azar, A.T., Radwan, A.G., Volos, C., Pham, V.T., et al., 2017c. Dead-
beat synchronization control in discrete-time chaotic systems. 2017 6th International
Conference on Modern Circuits and Systems Technologies (MOCAST). IEEE, pp. 1 4.
Panchuk, A., Sushko, I., Avrutin, V., 2015. Bifurcation structures in a bimodal piecewise linear
map: chaotic dynamics. Int. J. Bifurcation Chaos 25, 1530006.