The role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral operators to establish Minkowski fractional inequalities. Several other new and novel fractional integral inequalities are also established. Compared to the existing results, these fractional integral inequalities are more general and substantial enough to create new and novel results. M-E-K fractional integral operators have been previously applied for other purposes but have never been applied to the subject of this paper. These operators generalize a popular class of fractional integrals; therefore, this approach will open an avenue for new research. The smart properties of these operators urge us to investigate more results using them.

This research aims to develop generalized fractional integral inequalities by utilizing multiple Erdélyi–Kober (E–K) fractional integral operators. Using a set of j, with $(j\in \mathbb{N})$ positively continuous and decaying functions in the finite interval $a\le t\le x$, the Fox-H function is involved in establishing new and novel fractional integral inequalities. Since the Fox-H function is the most general special function, the obtained inequalities are therefore sufficiently widespread and significant in comparison to the current literature to yield novel and unique results.

The present paper deals with well-posedness and asymptotic stability for weakly coupled wave equations with a more general internal control of diffusive type. Owing to the semigroup theory of linear operator, the well-posedness of system is proved. Furthermore, we show a general decay rate result. The method is based on the frequency domain approach combined with multiplier technique.

The sun is a fundamental element of the natural environment, and kinetic equations are crucial mathematical models for determining how quickly the chemical composition of a star like the sun is changing. Taking motivation from these facts, we develop and solve a novel fractional kinetic equation containing Fermi–Dirac (FD) and Bose–Einstein (BE) functions. Several distributional properties of these functions and their proposed new generalizations are investigated in this article. In fact, it is proved that these functions belong to distribution space ${\mathcal{D}}^{\prime }$ while their Fourier transforms belong to ${\mathcal{Z}}^{\prime }.$ Fourier and Laplace transforms of these functions are computed by using their distributional representation. Thanks to them, we can compute various new fractional calculus formulae and a new relation involving the Fox–Wright function. Some fractional kinetic equations containing the FD and BE functions are also formulated and solved.

Fuzzy systems play a crucial role in emerging fields such as artificial intelligence, machine learning, and computer science, drawing significant research interest in fuzzy difference equations. Inspired by this, we analyze the dynamic properties of a fourth-order exponential Riccati-type fuzzy difference equation. The study is further extended to a system of fourth-order fuzzy difference equations. We investigate the boundedness, as well as the local and global stability, of positive solutions. To support the theoretical findings, numerical examples are presented along with graphical and tabular representations.