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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]

In this paper, we mainly focus on the existence of the mild solution for the Hilfer fractional differential inclusions with almost sectorial operators. By using the results on the fractional calculus, sectorial operators, semigroup theory, and Dhage's fixed point theorem, we prove the primary results. Finally, an example is presented to demonstrate the theory obtained. [ABSTRACT FROM AUTHOR]

In this study, we establish the approximate controllability of the Hilfer fractional neutral differential inclusions with infinite delay. The main result of this article is proven by applying some ideas of semigroup theory with fractional order and Dhage's fixed point theorem. Firstly, we prove the approximate controllability of the Hilfer fractional system. Next, we extend our study to the system with nonlocal conditions. Finally, theoretical and practical applications are presented to assist in the effectiveness of our discussion. [ABSTRACT FROM AUTHOR]

In this manuscript, we are mainly focusing on the existence of mild solutions for the Hilfer fractional evolution system with infinite delay via measures of noncompactness. Fractional calculus and fixed‐point approach are taken into consideration to study the primary outcomes. Finally, we extend the results to the existence of a neutral system with nonlocal conditions. Ultimately, a model is presented for illustration of theory. [ABSTRACT FROM AUTHOR]