Nanofluids have attracted significant research interest due to their diverse applications in biomedical engineering, energy systems, and thermal management

We study the exact partial controllability of a semilinear stochastic fractional evolution equation of Caputo order $\alpha \in (1,2)$ in a separable Hilbert space, subject to a genuine state-dependent delay $y(t-\rho (t,y_t))$, impulsive effects, and Q-Wiener perturbations. To accommodate the state-dependent delay, we work in a Sobolev-type prehistory space that restores the local Lipschitz property lost in the space of continuous functions, and to accommodate the impulses, we use a piecewise-continuous mean-square path space; two initial data points are prescribed, as required for $\alpha \in (1,2)$. The existence and uniqueness of mild solutions are established by the Banach contraction principle on a Lipschitz ball equipped with a Bielecki-type weighted norm, which removes the smallness conditions of the contraction-based literature. The stochastic convolution is treated rigorously by the Da Prato factorization realized through the subordination of the fractional resolvent family, with the Burkholder inequality applied only to the genuine Itô integral and never to the non-martingale convolution itself. For controllability, we adopt the correct stochastic notion: the target is an ${\mathcal{F}}_T$-measurable random variable, and the adapted control is constructed through the martingale representation theorem, together with the projected controllability Gramian, yielding $Py\left(T\right)=\eta$ almost surely. A numerical study on a stochastic fractional wave equation verifies the main controllability theorem, driving the projected terminal state to the prescribed ${\mathcal{F}}_T$-measurable target at machine precision, and confirms the observability requirement.

For $0\le \alpha <1$ and $\lambda \ge 0$, we introduce a filtered Janowski-rotated pseudo-Bazilević class of normalized analytic functions in the unit disk. The fractional power is defined through the unique analytic logarithm normalized at the origin, and a first-order differential filter is applied before the rotated Janowski subordination. Explicit formulae for $a_2$ and $a_3$ reduce the direct, logarithmic, inverse, and inverse-logarithmic Fekete–Szegő-type functionals to a common Schwarz coefficient template. We derive a fixed-$a_2$ variability disk for $a_3$, Janowski disk containment, a positive-real-part consequence, and branch-free reconstruction formulae. Sharpness and function-level realization are unconditional on the integrable slice $\alpha =0$. For $0<\alpha <1$, the variability disk is exact at the Schwarz-data level and is realized by a function whenever the explicitly reconstructed auxiliary function is nonvanishing. Numerical results, including a two-parameter surface, show the damping effect of $\lambda$ on the base coefficient scales and on representative complete bounds while also displaying their interaction with $\alpha$, the rotation, and the Janowski parameters.

This paper investigates the spatial analyticity of solutions to the Korteweg–de Vries equation and exploits this property to improve the efficiency of numerical modeling and to solve inverse problems. It is theoretically proven that the solutions of the Korteweg–de Vries equation belong to Gevrey spaces, and an estimate for the analyticity radius $\sigma \left(t\right)$ is derived, showing that it decays at an algebraic rate governed by $\sigma \left(t\right)\ge {\sigma }_0/(1+C{\sigma }_{0}t)$. This property ensures that the Fourier coefficients decay exponentially, which is leveraged to design an efficient spectral numerical scheme with exponentially small truncation error. A detailed convergence analysis demonstrates that the spectral method achieves exponential accuracy, significantly outperforming conventional finite-difference approaches. Furthermore, a reconstruction algorithm is developed to recover the full wave field from limited sensor data, achieving an $L^2$ error below ${10}^{-3}$ using only 10% of the spatial domain data. Extensive numerical experiments, including sensitivity analysis with respect to the estimated analyticity radius and comparison with finite-difference methods, confirm the theoretical predictions and demonstrate the robustness of the proposed approach. The results establish that spatial analyticity provides a powerful and practical framework for both forward modeling and data reconstruction in dispersive partial differential equations.