In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series numbers. The mean, or Kolmogorov–Nagumo generalizes the classical mean and appears in many disciplines, from information theory to physics, economics traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introd...

In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using Picard iteration method. Different from previous works, our paper presents a new theory fractional integral. We have proved convergence solution averaged HIDSFOS to that standard in sense mean square also probability. Some examples are given at end illustrate theoretical...

In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using Picard iteration method. The paper provides new results integral calculus techniques. We have shown convergence solution averaged PIDSFOS to that standard in context mean square also probability. One example is given illustrate our results.

This paper studies a maintenance policy for a system composed of two components, which are subject to continuous deterioration and consequently stochastic failure. The failure of each component results in the failure of the system. The components are inspected periodically and their deterioration degrees are monitored. The components can be maintained using different maintenance actions (repair...