Hybrid synchronization is one of the most significant aspects of a dynamic system. We achieve nonlinear control unit results to synchronize two comparable 7D structures in this study. Many dynamic systems are directly connected to health care and directly enhance health. We employed linearization and Lyapunov as analytical methods, and since the linearization method does not need updating the Lyapunov function, it is more successful in achieving synchronization phenomena with better outcomes than the Lyapunov method. The two methods were combined, and the result was a striking resemblance to the dynamic system’s mistake. The mathematical system with control and error of the dynamic system was subjected to digital emulation. The digital good outcomes were comparable to the two methods previously stated. We compared the outcomes of three hybrid synchronizations based on Lyapunov and linearization methods. Finally, we used the existing system, presenting it in a new attractor and comparing the findings to those of other similar systems.

A class of fractional-order differential models of RNA silencing with memory is presented in this paper. We also carry out a detailed analysis on the stability of equilibrium and we show that the model established in this paper possesses non-negative solutions. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. Numerical simulations are presented to illustrate the results. Also, the numerical simulations show that, modeling the phenomena of RNA silencing by fractional ordinary differential equations (FODE) has more advantages than classical integer-order modeling.

In this paper we will introduce new type of chaotic graphs, when vertices of these graphs are appearance like line and edges of these graphs are appearance like tape or ribbon and when these graphs carries physical characters . The representation of the chaotic graphs by matrices will be obtained. The transformations of the chaotic graph into itself and into another graphs will be discussed.Keywords: Chaotic, Graphs Definitions and background Abstract graphs:An abstract graphs G is a diagram consisting of a finite non empty set of the elements, called "vertices" denoted by V(G) together with a set of unordered pairs of these elements, called "edges" denoted by E(G). The set of vertices of the graph G is called "the vertex -set of G " and the list of edges is called "the edge -list of G " (Gibbons A., 1985), (Giblin P.J., 1977).

In this paper we will introduce new type of graphs, when vertices of these graphs are appearance like line and edges of these graphs are appearance like tape or ribbon.We introduce types of representation of the new graph by the adjacent and the incidence matrices and we will discuss their transformations

The aim of the study is to investigate the existence and uniqueness of solutions for a semi linear fractional differential system via Banach fixed point theorem. The study proved the existence and uniqueness of solution for a fractional differential system with initial conditions by using contraction mapping theorem, existence and uniqueness results are obtained. Some examples are chosen to illustrate the validity of our results.