Existence, Uniqueness and Stability of Fractional Order Stochastic Delay System

This chapter deals with the problem of fractional higher-order stochastic delay systems. A solution representation is given by using sin and cos matrix functions for different delay intervals. Further, existence and uniqueness results are proved through fixed point theorem. Moreover, finite-time stability criteria are obtained using fractional Gronwall-Bellman inequality lemma. Finally, numerical simulation is carried out to check the proposed theoretical results

Zinc homeostasis and signaling in health and diseases: Zinc signaling

The essential trace element zinc (Zn) is widely required in cellular functions, and abnormal Zn homeostasis causes a variety of health problems that include growth retardation, immunodeficiency, hypogonadism, and neuronal and sensory dysfunctions. Zn homeostasis is regulated through Zn transporters, permeable channels, and metallothioneins. Recent studies highlight Zn’s dynamic activity and its role as a signaling mediator. Zn acts as an intracellular signaling molecule, capable of communicating between cells, converting extracellular stimuli to intracellular signals, and controlling intracellular events. We have proposed that intracellular Zn signaling falls into two classes, early and late Zn signaling. This review addresses recent findings regarding Zn signaling and its role in physiological processes and pathogenesis