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In this study, we examine whether mild solutions to a fractional stochastic evolution system with a fractional Caputo derivative on an infinite interval exist and are attractive. We use semigroup theory, fractional calculus, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. There are several suggested sufficient requirements for the existence of mild solutions to the stated problem. Examples that highlight the key findings are provided. [ABSTRACT FROM AUTHOR]

This research aimed to design and analyse an improved membrane reactor insertion for CWAO technology to eradicate POPs and emerging contaminants in wastewater. Due to its chemical stability and high permeability coefficient, the reactor was fitted with polyvinylidene fluoride (PVDF) membranes. Pd/TiO2 catalysts were prepared by the wet impregnation method and incorporated into the CWAO process to improve the effectiveness of the degradation of pollutants at lower temperatures and pressures. Flexibility studies were then conducted, wherein the actual operating conditions of temperature, pressure, and oxygen feed rates were varied and the performance of the system was optimised to achieve the highest removal efficiency at the lowest energy requirements. Furthermore, the enhancement of photocatalysis incorporating UV lamp and titanium dioxide coated on the membrane enhanced the TOC reduction of 15%, or 70% only with the addition of photocatalytic reduction using the ceramic membrane-immobilised titanium dioxide after the CWAO step, which achieved only a 55% removal. Discussing fouling control approaches such as surface treatment and backflushing to improve performance over the long term. The performance of the system remained relatively constant over 1000 h, without any sign of decline in the catalytic properties of the catalysts or degradation of the membrane. LCA suggested that energy use was reduced by 20% compared to conventional processes and the economic analysis showed that operational costs are 25% lower. These findings establish the integrated membrane-CWAO system as a cost-effective, sustainable solution to large-scale industrial and municipal wastewater treatment by providing high pollutant removal efficiency that can be scaled up. [ABSTRACT FROM AUTHOR]

This article is mainly focusing on the approximate controllability of neutral integro‐differential stochastic equations with state‐dependent delay. The main results of this article are proved by applying some ideas about the semigroup theory and resolvent operators. At first, the investigation about the existence of a mild solution and then we discuss the approximate controllability of the considered system. Next, we extend our study to the system with non‐local conditions. Finally, a theoretical application is presented for proving the validity of controllability results obtained. [ABSTRACT FROM AUTHOR]

In our article, we primarily concentrate on the approximate controllability results for Sobolev type fractional stochastic evolution hemivariational inequalities. By applying the facts related to fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system. In the end, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]