A non-minimally coupled cosmological scenario is considered in the context of $f(R,T)=f_1\left(R\right)+f_2\left(R\right)f_3\left(T\right)$ gravity (with R being the Ricci scalar and T the trace of the energy-momentum tensor) in the background of the flat Friedmann–Robertson–Walker (FRW) model. The field equations of this modified theory are solved using a time-dependent deceleration parameter for a dust. The behavior of the model is analyzed taking into account constraints from recent observed values the deceleration parameter. It is shown that the analyzed models can explain the transition from the decelerating phase to the accelerating one in the expansion of the universe, by staying true to the results of the observable universe. It is shown that the models are dominated by a quintessence-like cosmological dark fluid at the late universe.

This paper is a parametrization of the equation of state (EoS) parameter of dark energy (DE), which is parameterized using square-root (SR) form i.e. ω SR = ω 0 + ω 1 z z 2 + 1 , where ω ₀ and ω ₁ are free constants. This parametrization is examined in the context of the recently suggested f(Q) gravity theory as an alternative to general relativity (GR), in which gravitational effects are attributed to the non-metricity scalar Q with the functional form f(Q) = Q + α Q ⁿ , where α and n are arbitrary constants. We derive observational constraints on model parameters using the Hubble dataset with 31 data points and the Supernovae (SNe) dataset from the Pantheon samples compilation dataset with 1048 data points. For the current model, the evolution of the deceleration parameter, density parameter, EoS for DE, and Om(z) diagnostic have all been investigated. It has been shown that the deceleration parameter favors the current accelerated expansion phase. It has also been shown that the EoS parameter for DE has a quintessence nature at this time.

The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the $({\displaystyle \frac{G^{\prime }}{G^{\prime }+G+A}})$-expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3D), contour, and two-dimensional (2D) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application.

As a follow-up of a recent article in which we investigated the cosmological background expansion history of the universe in Bianchi type-V cosmological models with bulk viscous fluid and evolving cosmological $\Lambda$ and Newtonian G parameters, we study the evolution of the cosmological perturbations in the current work. In particular, we analyse the evolution of the viscous matter over-density that leads to formation of large-scale structures in the Bianchi-V model, and compare the results with standard $\Lambda$CDM solutions. Our results suggest that introducing viscous fluid in the background described by Bianchi-V geometry with evolving $\Lambda$ and G amplifies the structure-growth rate.

This study introduces a novel four-dimensional hyperchaotic system characterized by two positive Lyapunov exponents, showcasing enhanced complexity compared to traditional chaotic systems. The model’s dynamics are analyzed through equilibrium points, dissipation, bifurcations, Lyapunov spectra, Kaplan-Yorke dimension, phase portraits, and Poincaré mapping. The system demonstrates hyperchaotic behavior and multi-scroll attractors under specific parameter conditions. Control and synchronization techniques are developed using feedback and adaptive methods, enabling secure communication applications. Numerical simulations validate the successful encoding and decoding of messages, highlighting the system’s potential for secure communication and encryption.

This research uses three analytical processes: the novel Kudryshov procedure, the direct algebraic approach, and the modified Kudryshov technique to acquire exact and analytical outcomes for the long–short wave interaction nonlinear problem. A variable transformation is applied to convert the system’s partial differential framework into an ordinary one. Thereafter, the governing model is analyzed using the methods mentioned above, which yield novel dynamic optical solitons. These solutions include bell-shaped solitons, multiple breathers with bright, dark, and dark–bright structures, as well as periodic breathers with bright, dark, and bright–dark forms. Demonstrated through stable solutions, these results validate the computational approach. Multistability and sensitivity are explored using employing planar dynamics. Various chaos-identifying tools such as bifurcation plots, return maps, Lyapunov exponents, and power spectrum plots are applied to test the chaotic analysis of the stated model. Moreover, quasi-periodic, periodic, and disordered patterns are derived from the presented equation. Additionally, graphical representations illustrate the dynamic aspects of the obtained solutions. Overall, the employed methodologies prove impactful, efficient, and relevant for tackling diverse nonlinear phenomena.