Explore the vast range of titles available.

In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana–Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers–Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana–Baleanu derivatives and an extended Adams–Bashforth–Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor.

The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized ( ψ , ϕ ) -contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of ( ψ , ϕ ) . Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of ψ and ϕ and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

This article investigates the stochastic Davey–Stewartson equations influenced by multiplicative noise within the framework of the It calculus. These equations are of significant importance because they extend the nonlinear Schrödinger equation into higher dimensions, serving as fundamental models for nonlinear phenomena in plasma physics, nonlinear optics, and hydrodynamics. This paper is motivated by the need to understand how random fluctuations affect soliton behavior in nonlinear systems. This is particularly relevant in applications such as turbulent plasma waves and optical fibers, where noise can significantly impact wave propagation. We employ the modified extended direct algebraic method for finding exact stochastic soliton solutions to the stochastic Davey–Stewartson equations. The study derives a class of exact stochastic soliton solutions, including dark, singular, rational, and periodic waves. MATLAB is used to provide visual representations of these stochastic soliton solutions through 3D surface plots, contour plots, and line plots. These solutions offer essential insights into how random disturbances influence nonlinear wave systems, particularly in turbulent plasma waves and optical fibers. To the best of our knowledge, the application of the modified extended direct algebraic method to the stochastic Davey–Stewartson equations with multiplicative noise, along with the subsequent analysis of the stabilizing effects on dark, singular, rational, and periodic stochastic soliton solutions is novel. The study demonstrates how multiplicative Brownian motion regulates these wave structures, providing new information on the impact of noise on higher-dimensional nonlinear systems.

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 (S1), individuals with high susceptibility (S2), infected individuals (I), exposed individuals (E), and recovered individuals (R). To capture the complex dynamics of EVD, we employ a Φ-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 Φ-Caputo derivative in the first interval and the Φ-ABC derivative in the second interval. The study determines the basic reproduction number R0, 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.

This research investigates the dynamics of nonlinear coupled hybrid systems using a modified Mittag–Leffler fractional derivative. The primary objective is to establish criteria for the existence and uniqueness of solutions through the implementation of Dhage’s hybrid fixed-point theorem. The study further analyzes the stability of the proposed model. To demonstrate the practical application of this framework, we utilize a modified Mittag–Leffler operator to model the transmission of the Ebola virus, known for its complex and diverse dynamics. The analysis is conducted using a combination of theoretical and numerical methods, including transforming the system of equations into an equivalent integral form, applying the fixed-point theorem, and developing a numerical scheme based on Lagrange’s interpolation for simulating the Ebola virus model. This study aims to enhance our understanding of Ebola virus dynamics and provide valuable insights for developing effective control strategies.

The major goal of this work is investigating sufficient conditions for the existence and uniqueness of solutions for implicit impulsive coupled system of φ-Hilfer fractional differential equations (FDEs) with instantaneous impulses and terminal conditions. First, we derive equivalent fractional integral equations of the proposed system. Next, by employing some standard fixed point theorems such as Leray–Schauder alternative and Banach, we obtain the existence and uniqueness of solutions. Further, by mathematical analysis technique we investigate the Ulam–Hyers (UH) and generalized UH (GUH) stability of solutions. Finally, we provide a pertinent example to corroborate the results obtained.

This study presents a novel numerical approach for approximating the solution of third-order pseudo-parabolic partial differential equations (PDEs), which exhibit both parabolic and hyperbolic characteristics. The proposed method employs a cubic trigonometric tension B-spline collocation technique for spatial discretization, offering greater flexibility and accuracy compared to traditional spline methods. For time discretization, the finite difference method (FDM) is used, ensuring computational efficiency. Unlike many existing methods, our approach is tailored to handle the complexity of third-order equations while maintaining stability and accuracy over large-scale problems. The method’s unconditional stability is confirmed through a detailed von Neumann stability analysis, making it particularly robust for long-term simulations. Two illustrative examples are presented to demonstrate the method’s superior accuracy and flexibility in handling complex boundary conditions, as well as its ability to manage large-scale problems without requiring restrictive time steps. Compared to the existing methods, the combination of trigonometric tension B-splines with FDM proves to be a powerful and reliable tool for solving higher-order pseudo-parabolic equations.

In this research paper, we dedicate our interest to an investigation of the sufficient conditions for the existence of solutions of two new types of a coupled systems of hybrid fractional differential equations involving ϕ-Hilfer fractional derivatives. The existence results are established in the weighted space of functions using Dhage’s hybrid fixed point theorem for three operators in a Banach algebra and Dhage’s helpful generalization of Krasnoselskii fixed- point theorem. Finally, simulated examples are provided to demonstrate the obtained results.

This research paper intends to investigate some qualitative analysis for a nonlinear Langevin integro-fractional differential equation. We investigate the sufficient conditions for the existence and uniqueness of solutions for the proposed problem using Banach’s and Krasnoselskii’s fixed point theorems. Furthermore, we discuss different types of stability results in the frame of Ulam–Hyers by using a mathematical analysis approach. The obtained results are illustrated by presenting a numerical example.