This paper presents a novel fractional-order model for glucose-insulin dynamics using the Caputo-Fabrizio (CF) derivative, which accounts for memory effects through its nonsingular exponential kernel. Existence and uniqueness of the solution are established via fixed point theory, and infinite series solutions are obtained using the Sumudu transform. Hyers-Ulam stability is analyzed to assess the system’s robustness against perturbations. A linear control strategy is introduced to regulate glucose levels, demonstrating potential for integration with real-time insulin delivery systems. Compared to classical integer-order models, the proposed approach provides improved accuracy, enhanced stability, and deeper insight into the chaotic behavior of glucose-insulin interactions. This framework supports the development of personalized diabetes treatment and adaptive control strategies.

This study presents a comprehensive analysis of zoonotic disease transmission dynamics between baboon and human populations using both deterministic and stochastic modeling approaches. The model is constructed with a symmetric compartmental structure for each species—susceptible, infected, and recovered—which reflects a biological and mathematical symmetry between the two interacting populations. Public health control strategies such as sterilization, restricted food access, and reduced human–baboon interaction are incorporated symmetrically, allowing for a balanced evaluation of their effectiveness across species. The basic reproduction number (${\mathcal{R}}_0$) is derived analytically and examined through sensitivity indices to identify critical epidemiological parameters. Numerical simulations, implemented via the Euler–Maruyama method, explore the influence of stochastic perturbations on disease trajectories. Statistical tools including Maximum Likelihood Estimation (MLE), Mean Squared Error (MSE), and Power Spectral Density (PSD) analysis validate model predictions and assess variability across noise levels. The results provide probabilistic confidence intervals and highlight the robustness of the proposed control strategies. This symmetry-aware, dual-framework modeling approach offers novel insights into zoonotic disease management, particularly in ecologically dynamic regions with frequent human–wildlife interactions.

This study applies the Multi-Step Generalized Differential Transform Method (MSGDTM) and the Jumarie-Stancu Collocation Series Method (JSCSM) to analyze a fractional-order Model (1). The model incorporates Caputo fractional derivatives to capture the nonlocal and memory-dependent characteristics of glucose-insulin interactions, considering physiological factors such as β- cell activity and external glucose intake. Stability analysis reveals bifurcations and chaotic attractors, demonstrating the system’s sensitivity to fractional orders. Numerical simulations compare MSGDTM and JSCSM accuracy and efficiency, highlighting MSGDTM’s superior convergence and lower approximation error. The results show that fractional-order modeling provides a more accurate framework for understanding glucose-insulin dynamics and predicting metabolic behavior. Furthermore, control mechanisms are introduced to mitigate chaos, offering potential strategies for managing diabetes. This work emphasizes the robustness of MSGDTM in solving complex fractional biological models. It provides insights into fractional calculus applications in biomedical research.

In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the influence of magnetic fields on weak ion-acoustic wave propagation. This research aims to achieve three main objectives. First, we uncover soliton solutions of the coupled system in hyperbolic, trigonometric, and rational forms, both in single and combined expressions. These results are obtained using the extended rational sinh-Gordon expansion method and the $\left({\displaystyle \frac{G^{\prime }}{G}},{\displaystyle \frac{1}{G}}\right)$-expansion method. Second, we analyze the dynamic characteristics of the model by performing bifurcation and sensitivity analyses and identifying the corresponding Hamiltonian function. To understand the mechanisms of intricate physical phenomena and dynamical processes, we plot 2D, 3D, and contour diagrams for appropriate parameter values. We also analyze the bifurcation of phase portraits of the ordinary differential equations corresponding to the investigated partial differential equation. The novelty of this study lies in the fact that the proposed model has not been previously explored using these advanced methods and comprehensive dynamical analyses.

This study investigates the geometry of osculating type-2 ruled surfaces in Minkowski 3-space ${\mathbf{E}}_1^3$, formulated through the Type-2 Bishop frame associated with a spacelike curve whose principal normal is timelike and binormal is spacelike. Using the hyperbolic transformation linking the Frenet–Serret and Bishop frames, we analyze how the Bishop curvatures ${\zeta }_1$ and ${\zeta }_2$ affect the geometric behavior and formation of such surfaces. Explicit criteria are derived for cylindrical, developable, and minimal configurations, together with analytical expressions for Gaussian and mean curvatures. We also determine the conditions under which the base curve behaves as a geodesic, asymptotic line, or line of curvature. Several illustrative examples in Minkowski 3-space are provided to visualize the geometric influence of ${\zeta }_1$ and ${\zeta }_2$ on flatness, minimality, and developability. Overall, the Type-2 Bishop frame offers a smooth and effective framework for characterizing Lorentzian geometry and symmetry of osculating ruled surfaces, extending classical Euclidean results to the Minkowski setting.

In Minkowski 3-space, we establish a geometric framework to osculate Type-II ruled surfaces by utilizing the Type-II Bishop frame in $\left({\mathbb{E}}_1^3\right)$. Our analysis extends to higher-order singularities such as butterflies and pyramids, including explicit singularity loci. We also compare Type-II Bishop frames with rotation-minimizing frames using timelike base curves and spacelike normals. With RK4 integration, we develop a robust computational model for Weingarten surfaces and subclasses with constant curvature. The theoretical foundation for Type-II Bishop frames is extended to higher-dimensional Minkowski spaces ${\mathbb{E}}_1^n$ for $n>3$ through generalized Frenet-type equations and curvature functions. We determine exact stability conditions under perturbations of Bishop curvature using advanced singularity theory. The numerical implementations of our methods, including geometric modeling and relativistic geometry, demonstrate their effectiveness in both theoretical and applied contexts.