Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with low susceptibility (${\mathbb{S}}_1$), individuals with high susceptibility (${\mathbb{S}}_2$), infected individuals ($\mathbb{I}$), exposed individuals ($\mathbb{E}$), and recovered individuals ($\mathbb{R}$). To capture the complex dynamics of EVD, we employ a $\Phi$-piecewise hybrid fractional derivative approach. We investigate the crossover effect and its impact on disease dynamics by dividing the study interval into two subintervals and utilize the $\Phi$-Caputo derivative in the first interval and the $\Phi$-ABC derivative in the second interval. The study determines the basic reproduction number ${\mathit{R}}_0$, analyzes the stability of the disease-free equilibrium and investigates the sensitivity of the parameters to understand how variations affect the system’s behavior and outcomes. Numerical simulations support the model and demonstrate consistent results with the theoretical analysis, highlighting the importance of fractional calculus in modeling infectious diseases. This research provides valuable information for developing effective control strategies to combat EVD.

In this research, we define a few subclasses of analytic functions which are connected to sine functions and the cardioid domain in the unit disk. We investigate initial coefficient bounds, the Fekete–Szego problem and second and third Hankel determinants for the functions f belonging to these newly defined classes. We also define the class of m-fold symmetric functions related with the sine function and then investigate the bounds of the third Hankel determinant for twofold symmetric and threefold symmetric functions.

The concept of A-curves is considered as a novel application of real field extensions in solving some algebraic vectorial equations defined by Euclidean norms. In this paper, we present a novel insight through the classification of A-curves by illustrating many new semi-module isomorphisms between the direct product of weak fuzzy complex numbers with itself and the direct product of classical Euclidean vector spaces multiplied by itself. These isomorphisms will give us a full classification of A-curves that are related to weak fuzzy complex ring. Also, we provide many examples to explain the contribution of our work.

This article contains some relations, which include some embedding and transition properties, between the Muckenhoupt classes ${\mathcal{M}}_{\gamma };$$\gamma >1$ and the Gehring classes ${\mathcal{G}}_{\delta };$$\delta >1$ of bi-Sobolev weights on a time scale $\mathbb{T}$. In addition, we establish the relations between Muckenhoupt and Gehring classes, where we define a new time scale $\tilde{\mathbb{T}}=v\left(\mathbb{T}\right)$, to indicate that if the $\tilde{\Delta }$ derivative of the inverse of a bi-Sobolev weight belongs to the Gehring class, then the $\Delta$ derivative of a bi-Sobolev weight on a time scale $\mathbb{T}$ belongs to the Muckenhoupt class. Furthermore, our results, which will be established by a newly developed technique, show that the study of the properties in the continuous and discrete classes of weights can be unified. As special cases of our results, when $\mathbb{T}=\mathbb{R}$, one can obtain classical continuous results, and when $\mathbb{T}=\mathbb{N}$, one can obtain discrete results which are new and interesting for the reader.

American scientific publishing group

We study the classical and free cumulants of the $\omega$-Gaussian central limit laws arising from braidable quantum coin tosses. Taking the known central limit theorem and oriented-pairing moment formula as input, we carry out a cumulant-level analysis of the resulting laws. At the imaginary parameter, we show that the first obstruction to semicircularity occurs at the eighth free cumulant, thereby identifying precisely where the limiting law first departs from semicircular behavior. Near the Gaussian endpoint, we prove that all higher even classical cumulants of order at least six vanish to at least second order. We further compute the classical cumulants through even order 16 and find a stronger order-dependent vanishing pattern, indicating increasing cancellation at the Gaussian endpoint as the cumulant order grows. These results reveal higher-order effects of the underlying quantum braiding that are not apparent from the first few moments alone and lead to an all-order divisibility conjecture together with several related open problems for the oriented-pairing expansion.