In this study, we developed a Caputo-Fractional Chlamydia pandemic model to describe the disease’s spread. We demonstrated the model’s positivity and boundedness, ensuring biological relevance. The existence and uniqueness of the model’s solution were established, and we investigated the stability of the $$\alpha$$ -fractional order model. Our analysis proved that the disease-free equilibrium point is locally asymptotically stable. Additionally, we showed that the model has a single endemic equilibrium point, which is globally asymptotically stable when $${\mathscr {R}}_0$$ exceeds 1. Using Latin Hypercube sampling and partial rank correlation coefficients (PRCCs), sensitivity analysis identified key parameters influencing $${\mathscr {R}}_0$$ . Numerical simulations further illustrated the impact of parameter variations on disease dynamics.

This article investigates the impacts of varying thermal conductivity in the semi-infinite medium due to laser heating sources with a timed pulse. The governing formulations are based on a Lord-Shulman (LS) thermoelastic model with one thermal relaxation time under changing thermal conductivity. To study the nonlinear problems and get the governing formulations, the time-domain finite element approach is used. Laplace transforms and the eigenvalues method are used to solve the problem in the linear case implementation. The impacts of varying thermal relaxation time, time duration of a laser pulse and thermal conductivity are investigated. The numerical outcome obtained through the finite element approach are compared with analytical solutions for constant thermal conductivity to validate the precision of the numerical solution. The numerical results of temperature, stress, and displacement variation are presented graphically.

This paper focuses on studying the oscillatory properties of a distinctive class of second-order advanced differential equations with distributed deviating arguments in a noncanonical case. Utilizing the Riccati method and the comparison method with first-order equations, in addition to other analytical methods, we have established criteria to test whether the solutions of the studied equation exhibit oscillatory behavior. To verify the validity of the results we obtained and determine their applicability, we present some examples to confirm the strength and accuracy of our proposed criteria.

In this work, the novel general formula for a time-dependent nuclear reactor system of equations with delayed neutron effect has been formulated using a fractional calculus model. We explore the properties of this model, including two analytical approximation methods, the Temimi–Ansari method (TAM) and the Sumudu residual power series method (SRPSM), for solving the equation. These methods allow for the computation of approximate solutions at specific points. This is particularly useful for partial differential equations (PDEs) arising in various fields like physics, engineering, and finance. This work is hoped to improve the advancement of nuclear modeling and simulation, providing researchers and engineers with a powerful mathematical tool for studying the complex dynamics of these critical energy systems.