[1] C. Goodrich and A.C. Peterson: Discrete Fractional Calculus. Springer: Berlin, Germany, 2015, ISBN 978-3-319-79809-7.
[2] P. Ostalczyk: Discrete Fractional Calculus: Applications in Control and Image Processing. World Scientific, 2016.
[3] K. Oprzedkiewicz and K. Dziedzic: Fractional discrete-continuous model of heat transfer process. Archives of Control Sciences, 31(2), (2021), 287– 306, DOI: 10.24425/acs.2021.137419.
[4] T. Kaczorek and A. Ruszewski: Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks. Archives of Control Sciences, 30(4), (2020), 667–681, DOI: 10.24425/acs.2020.135846.
[5] J.B. Diaz and T.J. Olser: Differences of fractional order. Mathematics of Computation, 28 (1974), 185–202, DOI: 10.1090/S0025-5718-1974-0346352-5.
[6] F.M. Atici and P.W. Eloe: A transform method in discrete fractional calculus. International Journal of Difference Equations, 2 (2007), 165–176.
[7] F.M. Atici and P.W. Eloe: Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed. I, 3 , (2009), 1–12.
[8] G. Anastassiou: Principles of delta fractional calculus on time scales and inequalities. Mathematical and Computer Modelling, 52(3-4), (2010), 556– 566, DOI: 10.1016/j.mcm.2010.03.055.
[9] T. Abdeljawad: On Riemann and Caputo fractional differences. Computers and Mathematics with Applications, 62(3), (2011), 1602–1611, DOI: 10.1016/j.camwa.2011.03.036.
[10] M. Edelman, E.E.N. Macau, and M.A.F. Sanjun (Eds.): Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Springer International Publishing, 2018.
[11] G.C. Wu, D. Baleanu, and S.D. Zeng: Discrete chaos in fractional sine and standard maps. Physics Letters A, 378(5-6), (2014), 484–487, DOI: 10.1016/j.physleta.2013.12.010.
[12] G.C. Wu and D. Baleanu: Discrete fractional logistic map and its chaos. Nonlinear Dynamics, 75(1-2), (2014), 283–287, DOI: 10.1007/s11071-013-1065-7.
[13] T. Hu: Discrete chaos in fractional Henon map. Applied Mathematics, 5(15), (2014), 2243–2248, DOI: 10.4236/am.2014.515218.
[14] G.C. Wu and D. Baleanu: Discrete chaos in fractional delayed logistic maps. Nonlinear Dynamics, 80 (2015), 1697–1703, DOI: 10.1007/s11071-014-1250-3.
[15] M.K. Shukla and B.B. Sharma: Investigation of chaos in fractional order generalized hyperchaotic Henon map. International Journal of Electronics and Communications, 78 (2017), 265–273, DOI: 10.1016/j.aeue.2017.05.009.
[16] A. Ouannas, A.A. Khennaoui, S. Bendoukha, and G. Grassi: On the dynamics and control of a fractional form of the discrete double scroll. International Journal of Bifurcation and Chaos, 29(6), (2019), DOI: 10.1142/S0218127419500780.
[17] L. Jouini, A. Ouannas, A.A. Khennaoui, X. Wang, G. Grassi, and V.T. Pham: The fractional form of a new three-dimensional generalized Henon map. Advances in Difference Equations, 122 (2019), DOI: 10.1186/s13662-019-2064-x.
[18] F. Hadjabi, A. Ouannas,N. Shawagfeh, A.A. Khennaoui, and G. Grassi: On two-dimensional fractional chaotic maps with symmetries. Symmetry, 12(5), (2020), DOI: 10.3390/sym12050756.
[19] D. Baleanu, G.C. Wu, Y.R. Bai, and F.L. Chen: Stability analysis of Caputo-like discrete fractional systems. Communications in Nonlinear Science and Numerical Simulation, 48 (2017), 520–530, DOI: 10.1016/j.cnsns.2017.01.002.
[20] A-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, X. Wang, V-T. Pham, and F.E. Alsaadi: Chaos, control, and synchronization in some fractional-order difference equations. Advances in Difference Equations, 412 (2019), DOI: 10.1186/s13662-019-2343-6.
[21] A. Ouannas, A.A. Khennaoui, G. Grassi, and S. Bendoukha: On chaos in the fractional-order Grassi-Miller map and its control. Journal of Computational and Applied Mathematics, 358(2019), 293–305, DOI: 10.1016/j.cam.2019.03.031.
[22] A. Ouannas, A.A. Khennaoui, S. Momani, G. Grassi and V.T. Pham: Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization. AIP Advances, 10 (2020), DOI: 10.1063/5.0004884.
[23] A. Ouannas, A-A. Khennaoui, S. Momani, G. Grassi, V-T. Pham, R. El- Khazali, and D. Vo Hoang: A quadratic fractional map without equilibria: Bifurcation, 0–1 test, complexity, entropy, and control. Electronics, 9 (2020), DOI: 10.3390/electronics9050748.
[24] A. Ouannas, A-A. Khennaoui, S. Bendoukha, Z.Wang, and V-T. Pham: The dynamics and control of the fractional forms of some rational chaotic maps. Journal of Systems Science and Complexity, 33 (2020), 584–603, DOI: 10.1007/s11424-020-8326-6.
[25] A-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, R.P. Lozi, and V-T. Pham: On fractional-order discrete-time systems: Chaos, stabilization and synchronization. Chaos, Solitons and Fractals, 119(C), (2019), 150– 162, DOI: 10.1016/j.chaos.2018.12.019.
[26] A. Ouannas, A-A. Khennaoui, Z. Odibat, V-T. Pham, and G. Grassi: On the dynamics, control and synchronization of fractional-order Ikeda map. Chaos, Solitons and Fractals, 123(C), (2015), 108–115, DOI: 10.1016/j.chaos.2019.04.002.
[27] A. Ouannas, F. Mesdoui, S. Momani, I. Batiha, and G. Grassi: Synchronization of FitzHugh-Nagumo reaction-diffusion systems via onedimensional linear control law. Archives of Control Sciences, 31(2), 2021, 333–345, DOI: 10.24425/acs.2021.137421.
[28] Y. Li, C. Sun, H. Ling, A. Lu, and Y. Liu: Oligopolies price game in fractional order system. Chaos, Solitons and Fractals, 132(C), (2020), DOI: 10.1016/j.chaos.2019.109583.
[29] D. Mozyrska and E. Girejko: Overview of fractional h-difference operators. In Advances in harmonic analysis and operator theory. Birkhäuser, Basel, 2013, 253–268.

[1] Merlin A., Back H., Search for a minimal-loss operating spanning tree configuration in an urban power distribution system, Fifth Power Systems Computer Conference (PSCC), Cambridge, Britain, pp. 1–18 (1975).
[2] Kashem M.A., Ganapathy V., Jasmon G.B., Network reconfiguration for load balancing in distribution networks, IEE Proceedings-Generation Transmission and Distribution, vol. 146, no. 6, pp. 563–567 (1999).
[3] Liu Y.K., Li J., Wu L., Coordinated Optimal Network Reconfiguration and Voltage Regulator/DER Control for Unbalanced Distribution Systems, IEEE Transactions on Smart Grid, vol. 10, no. 3, pp. 2912–2922 (2019).
[4] Ahmadi S., Vahidinasab V., Ghazizadeh M. et al., Co-optimising distribution network adequacy and security by simultaneous utilisation of network reconfiguration and distributed energy resources, IET Generation Transmission & Distribution, vol. 13, no. 20, pp. 4747–4755 (2019).
[5] Liu H.Q., Qu J.M., Shanshan Yang S.S. et al., Intelligent optimal dispatching of active distribution network using modified flower pollination algorithm, Archives of Electrical Engineering, vol. 69, no. 1, pp. 159–174 (2020).
[6] Rahman Y.A., Manjang S., Yusran et al., Distributed generation’s integration planning involving growth load models by means of genetic algorithm, Archives of Electrical Engineering, vol. 67, no. 3, pp. 667–682 (2018).
[7] Olamaei J., Niknam T., Gharehpetian G., Application of particle swarm optimisation for distribution feeder reconfiguration considering distributed generators, Applied Mathematics and Computation, vol. 201, no. 1, pp. 575–586 (2008).
[8] Tang H.L., Wu J., Multi-objective coordination optimisation method for DGs and EVs in distribution networks, Archives of Electrical Engineering, vol. 68, no. 1, pp. 15–32 (2019).
[9] Rao R.S., Ravindra K., Satish K. et al, Power loss minimization in distribution system using network reconfiguration in the presence of distributed generation, IEEE Transactions on Power Systems, vol. 28, no. 1, pp. 317–325 (2013).
[10] Ling F.H., Zhang J.H., Sun X.B. et al., The application based on improved FOA optimisation algorithm in distribution network reconfiguration, Electric Switchgear, vol. 57, no. 1, pp. 91–95 (2019).
[11] Singh D., Misra R.K., Multi-objective feeder reconfiguration in different tariff structures, IET Generation Transmission & Distribution, vol. 4, no. 8, pp. 974–988 (2010).
[12] Sun K.M., Chen Q., Zhao P., Genetic algorithm with mesh check for distribution network topology reconfiguration, Automation of Electric Power Systems, vol. 42, no. 11, pp. 64–71 (2018).
[13] Ganesh S., Kanimozhi R., Meta-heuristic technique for network reconfiguration in distribution system with photovoltaic and D-STATCOM, IET Generation, Transmission & Distribution, vol. 12, no. 20, pp. 4524–4535 (2018).
[14] Chen D.Y., Zhang X.X., Distribution network reconfiguration of distributed generation based on AMOPSO algorithm, Acta Energiae Solaris Sinica, vol. 38, no. 8, pp. 2195–2203 (2017).
[15] Li Z.K., Lu Q., Fu Y. et al., State split multi-objective dynamic programming algorithm for dynamic reconfiguration of active distribution network, Proceedings of the CSEE, vol. 39, no. 17, pp. 5025-5036 (2019).
[16] Ding Y., Wang F., Bin F. et al., Multi-objective distribution network reconfiguration based on game theory, Electric power automation equipment, vol. 39, no. 2, pp. 28–35 (2019).
[17] Li H.J., Zhang P.W., Guo H.D., Adaptive multi-objective particle swarm optimisation algorithm based on population Manhattan distance, Computer Integrated Manufacturing Systems, vol. 26, no. 4, pp. 1019–1032 (2020).
[18] Liao J.Q., Wang H., Wang X.P., Fruit fly optimisation algorithm with chaotic dynamical step factor, Transducer and Microsystem Technologies, vol. 38, no. 8, pp. 139–142 (2019).
[19] Marko M., Najdan V., Milica P. et al., Chaotic fruit fly optimisation algorithm, Knowledge-based systems, vol. 89, no. 11, pp. 446–458 (2015).
[20] Saffar A., Hooshmand R., Khodabakhshian A., A new fuzzy optimal reconfiguration of distribution systems for loss reduction and load balancing using ant colony search-based algorithm, Applied Soft Computing, vol. 11, no. 5, pp. 4021–4028 (2011).
[21] ZhaoY.L., Lu J.X.,Yan Q. et al., Research on 3D-U intelligent manufacturing cell facilities layout based on self-adapting multi-objective fruit fly optimisation algorithm, Computer Integrated Manufacturing Systems, vol. 8, no. 1, pp. 1–21 (2020).
[22] Deb K., Pratap A., Agarwal S. et al., A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197 (2002).
[23] Coello C.A.C., Pulido G.T., Lechuga M.S., Handling multiple objective with particle swarm optimisation, IEEE Transactions Evolutionary Computation, vol. 8, no. 3, pp. 256–279 (2004).
[24] Zitzler E., Deb K., Thiele L., Comparison of multi-objective evolutionary algorithms: empirical study, Evolutionary Computation, vol. 8, no. 8, pp. 173–195 (2000).
[25] Baran M.E., Wu F.F., Network reconfiguration in distribution systems for loss reduction and load balancing, IEEE Transactions on Power Delivery, vol. 4, no. 2, pp. 1401–1407 (1989).