In this paper, we introduce a generalized complex discrete fractional-order cosine map. Dynamical analysis of the proposed complex fractional order map is examined. The existence and stability characteristics of the map’s fixed points are explored. The existence of fractal Mandelbrot sets and Julia sets, as well as their fractal properties, are examined in detail. Several detailed simulations illustrate the effects of the fractional-order parameter, as well as the values of the map constant and exponent. In addition, complex domain controllers are constructed to control Julia sets produced by the proposed map or to achieve synchronization of two Julia sets in master/slave configurations. We identify the more realistic synchronization scenario in which the master map’s parameter values are unknown. Finally, numerical simulations are employed to confirm theoretical results obtained throughout the work.

As is well known the novel coronavirus (COVID-19) is a zoonotic virus and our model is concerned with the effect of the zoonotic source of the coronavirus during the outbreak in China. We present a SEIS complex network epidemic model for the novel coronavirus. Our model is presented in fractional form and with varying population. The steady states and the basic reproductive number are calculated. We also present some numerical examples and the sensitivity analysis of the basic reproductive number for the parameters.

This paper suggested a decision-making model for evaluating and raking the ecological and water resources under climate change. The environmental and water resources have different criteria, so multi-criteria decision-making (MCDM) is used to deal with conflict criteria. The MCDM methodology integrated with the fuzzy sets to deal with uncertainty and vague information. The weights of the requirements are computed by the average method. The VIKOR method is used to rank the alternatives. This study used 11 criteria and 10 alternatives. The results show that alternative 10 is the best and alternative 2 is the worst. The sensitivity analysis was conducted in two parts; in the first part, the criteria weights are changed into 12 cases, and then the rank of alternatives is computed to show the stability of the results. The value of v in the VIKOR method is changed in the second part, and then the rank of alternatives is computed. The results show that the rank of other options is stable in different cases.