In this research article, a nonlinear time–space fractional order (4+1)-dim Fokas wave equation that is crucial for examining the corporal marvels of waves on and inside the surface of water is examined. For this purpose, a well-known analytical method is utilized, namely, the Sardar sub-equation (SSE) method along with a truncated M-fractional derivative. As a result, many new families of solitary wave solutions, such as kink-type solitons, singular and periodic solitons, dark and bright solitons, are established. By using the SSE method, the outcomes are portrayed in 3-dim, 2-dim, and contour plots for distinct parametric values. The attained hyperbolic and trigonometric function-type results demonstrate the capability of recognizing the exact solutions of the other nonlinear evolution equations through the executed technique.

In this investigation, we first establish new quantum Hermite–Hadamard type integral inequalities for s-convex functions by utilizing newly defined $T_q$-integrals. Then, by using obtained inequality, we establish a new Hermite–Hadamard inequality for coordinated $\left(s_1,s_2\right)$-convex functions. The results obtained in this paper provide significant extensions of other related results given in the literature. Finally, some examples are given to illustrate the result obtained in this paper. These types of analytical inequalities, as well as solutions, apply to different areas where the concept of symmetry is important.

Modeling and design of on-chip interconnect, the interconnection between the components is becoming the fundamental roadblock in achieving high-speed integrated circuits. The scaling of interconnect in nanometer regime had shifted the paradime from device-dominated to interconnect-dominated design methodology. Driven by the expanding complexity of on-chip interconnects, a passivity preserving model order reduction (MOR) is essential for designing and estimating the performance for reliable operation of the integrated circuit. In this work, we developed a new frequency selective reduce norm spectral zero (RNSZ) projection method, which dynamically selects interpolation points using spectral zeros of the system. The proposed reduce-norm scheme can guarantee stability and passivity, while creating the reduced models, which are fairly accurate across selected narrow range of frequencies. The reduced order results indicate preservation of passivity and greater accuracy than the other model order reduction methods.

In this investigation, we established some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using the notion of 〖(p,q)〗^b-integeral .The perseverance of this article is to establish different results on the left hand side of 〖(p,q)〗^b- Hermite-Hadamard inequality for differentiable convex function along with critical a point. Some Special cases are obtain for different 〖(p,q)〗^b- Hermite Hadamard inequalies at critical point c for some specific values of q.

The generalized (3+1)-dimensional fractional q-deformed tanh-Gordon model and its optical solutions are studied under various physical conditions. Verifying our analytical findings and using the modified Sardar-sub equation technique (SSET) to examine the behavior of the governing model through convergence criteria under different parameters of the hyperbolic local derivative. By generating diverse optical phenomena and flexibility of the governing model, our findings pave the way for additional theoretical and applied physics research. The objective is also to study the bifurcation and chaotic behavior of the equation. To accomplish this, a dynamical system is created using the Galilean transformation. Analyzing the bifurcation and chaotic structure of the equation to identify important transitions that lead to chaotic behavior, and using phase-space analysis to understand the system's unpredictability. The study shows how small adjustments can have a significant effect on the results. This study clarifies the behavior of the model, which is crucial for several applications in quantum mechanics, physics, and optics.