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This article discusses changes in heat transfer resulting from laser pulses and magnetic fields produced in thermoelastic materials under initial stress. This paper introduces a novel approach to modeling generalized thermoelastic materials by including fractional time derivatives with Eringen's non‐local thermoelastic theory. This model incorporates both the Caputo–Fabrizio and the Atangana–Baleanu derivatives, which are novel forms of fractional derivatives in the domain of fractional calculus. Analytical formulations for system variables, such as temperature and thermal stress, were derived using the Laplace transform method. This was done considering the effects of laser pulses, non‐local actuators, and fractional actuators. The findings of these investigations are showcased through numerical illustrations and visual representations. The research also included comparisons between the acquired results and those derived from earlier theories, which may be regarded as a specific instance. Validating the suggested model and showing its correctness and applicability is seen as a crucial step. [ABSTRACT FROM AUTHOR]

This study primarily seeks to expand upon these developments by encompassing neutral differential equations of mixed type, incorporating both delay and advanced terms, particularly in the case of the canonical operator. The presented results are derived from the application of the comparison method, Riccati transformation, and integral averaging technique. These methodologies lead to substantial improvements and extensions of existing results found in the literature. Additionally, illustrative examples are provided to demonstrate the practical implications of the developed criteria. [ABSTRACT FROM AUTHOR]

The main aim of this study was to apply an analytical method to solve a nonlinear system of fractional differential equations (FDEs). This method is the Adomian decomposition method (ADM), and a comparison between its results was made by using a numerical method: Runge-Kutta 4 (RK4). It is proven that there is a unique solution to the system. The convergence of the series solution is given, and the error estimate is also proven. After that, the susceptible-infected-recovered (SIR) model was taken as an real phenomenon with such systems. This system is discussed with three different fractional derivatives (FDs): the Caputo-Fabrizio derivative (CFD), the Atangana-Baleanu derivative (ABD), and the Caputo derivative (CD). A comparison between these three different derivatives is given. We aimed to see which one of the new definitions (ABD and CFD) is close to one of the most important classical definitions (CD). [ABSTRACT FROM AUTHOR]