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In this paper, we establish iterative Hille-type criteria for advanced functional half-linear dynamic equations of the second order. These results extend and improve recent criteria established by multiple authors for the same equation and encompass classical criteria. We provide an example to demonstrate the significance of the results obtained. [ABSTRACT FROM AUTHOR]

Investigating the jounce vector in planar and space motion is the primary objective of this paper. For planar motion, the jounce vector is split into tangential‐normal and radial‐transverse components. Simple pendulum oscillation, a central force proportionate to distance, and Keplerian orbital motion are used as models for plane motion to show the geometric properties of the jounce vector. The jounce vector of a particle that is moving across three dimensions of Euclidean space is also investigated, and it is resolved in the tangential, radial, and other radial directions in the rectifying and osculating planes, respectively. The models used were an electron in a uniform magnetic field and a particle traveling along a spiral path. [ABSTRACT FROM AUTHOR]

In this paper, we look at the (4 + 1)‐dimensional stochastic Fokas equation (SFE) perturbed in the Itô sense by white noise. The tanh‐coth method and mapping method are used to acquire new trigonometric, hyperbolic, elliptic, and rational stochastic solutions. Also, we extend some earlier studies. Because the SFE equation is essential for describing different phenomena in ocean engineering, fluid mechanics and optics, the solutions obtained are useful in interpreting certain fascinating physical phenomena. To demonstrate how the multiplicative white noise affects the exact solutions of the SFE, we plot our figures in MATLAB and show several 3D graphical representations. We demonstrate how the solutions of SFE are stabilized by multiplicative white noise. [ABSTRACT FROM AUTHOR]