In this paper, two types of soft sets in soft ideal topological spaces
are introduced and some of their properties are discussed. The concept
of soft condense ideals is characterized by these collections of sets.
Also, some properties of soft extremally disconnected spaces are investigated.
Furthermore, decompositions of some types of soft continuous
mappings are given and some equivalent conditions concerning this
topic are established here.

This paper introduces the chaotic fractional-order Sprott Q system and its dynamics. The double compound combination of eight fractional-order chaotic synchronizations was investigated. This kind of synchronization is considered a generalization of many types of synchronization given in the literature. The analytical formula of the control functions is developed and proven using the tracking control method. As we know the fractional derivatives of two multiple functions are very difficult to calculate, and the tracking control method is more suitable for this kind of synchronization. This technique’s communication is more secure and reliable because there are more drive and response systems. To achieve the proposed synchronization, four driving and four response identical chaotic systems are used as an example. This scheme may be used in many applications such as secure communications and safe information. Using the proposed double compound-combination synchronization is an example given to encrypt a message. The analytical results were confirmed by numerical simulation, and we found good agreemen