Fractional Cesaro Matrix and its Associated Sequence Space

In this research, we introduce a new fractional Cesaro matrix and investigate the topological properties of the sequence space associated with this matrix. We also introduce a fractional Gamma matrix as well and obtain some factorizations for the Hilbert operator based on Cesaro and Gamma matrices. The results of these factorizations are two new inequalities one of which is a generalized version of the well-known Hilbert's inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.WOS:0006406030000012-s2.0-8510226707

Cesaro Spaces and Norm of Operators on These Matrix Domains

In this paper, we investigate some properties of the domain of the Cesaro matrix of ordernand compute Kothe dual of this space. Moreover, we compute the norm of well-known operators such as Hilbert, Hausdorff, backward difference and weighted mean operators on this new sequence space.WOS:0005459963000032-s2.0-8508693198

Fuzzy Sliding Mode Control for Hyper Chaotic Chen System

In this paper, a fuzzy sliding mode control method is proposed for stabilizing hyper chaotic Chen system. The main objective of the control scheme is to stabilize unstable equilibrium point of the system by controlling the states of the system so that they converge to a pre-defined sliding surface and remain on it. A fuzzy control technique is also utilized in order to overcome the main disadvantage of sliding mode control methods, i.e. chattering problem. It is shown that the equilibrium point of the system is stabilized by using the proposed method. A stability analysis is also performed to prove that the states of the system converge to the sliding surface and remain on it. Simulations show that the control method can be effectively applied to Chen system when it performs hyper chaotic behavior