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This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

In the present article, the three-phase-lag (3PHL) model and the Green-Naghdi theory of types II, III with memory-dependent derivative is used to study the effect of rotation on a nonlocal porous thermoelastic medium.

In this study normal mode analysis is used to obtain analytical expressions of the physical quantities. The numerical results are given and presented graphically when mechanical force is applied.

The model is illustrated in the context of the Green-Naghdi theory of types II, III and the three-phase lags model. Expressions for the physical quantities are solved by using the normal mode analysis and represented graphically.

Comparisons are made with the results predicted in the absence and presence of the rotation as well as a nonlocal parameter. Also, the comparisons are made with the results of the 3PHL model for different values of time delay.

The purpose of this paper is to introduce the phase-lag models (Lord-Shulman, dual-phase-lag and three-phase-lag) to study the effect of memory-dependent derivative and the influence of thermal loading due to laser pulse on the wave propagation of generalized micropolar thermoelasticity. The bounding plane surface is heated by a non-Gaussian laser beam with a pulse duration of 10 nanoseconds.

The normal mode analysis technique is used to obtain the exact expressions for the displacement components, the force stresses, the temperature, the couple stresses and the micro-rotation. Comparisons are made with the results predicted by three theories of the authors’ interest. Excellent predictive capability is demonstrated at a different time also.

The effect of memory-dependent derivative and the heat laser pulse on the displacement, the temperature distribution, the components of stress, the couple stress and the microrotation vector have been depicted graphically.

Some particular cases are also deduced from the present investigation.

The numerical results are presented graphically and are compared with different three theories for both in the presence and absence of memory-dependent effect and with the results predicted under three theories for two different values of the time.

The purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD).

The two-dimensional equations of generalized thermoelasticity with MDD are solved using a state-space approach. The numerical inversion method is employed for the inversion of Laplace and Fourier transforms.

The solutions are presented graphically for different values of time delay and kernel function.

The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of an isotropic plate.

This paper aims to study the energy ratios of plane waves on an imperfect interface of elastic half-space (EHS) and orthotropic piezothermoelastic half-space (OPHS).

The dual-phase lag (DPL) theory with memory-dependent derivatives is employed to study the variation of energy ratios at the imperfect interface.

A plane longitudinal wave (P) or transversal wave (SV) propagates through EHS and strikes at the interface. As a result, two waves are reflected, and four waves are transmitted, as shown in Figure 2. The amplitude ratios are determined by imperfect boundaries having normal stiffness and transverse stiffness. The variation of energy ratios is computed numerically for a particular model of graphite (EHS)/cadmium selenide (OPHS) and depicted graphically against the angle of incidence to consider the effect of stiffness parameters, memory and kernel functions.

The energy distribution of incident P or SV waves among various reflected and transmitted waves, as well as the interaction of waves for imperfect interface (IIF), normal stiffness interface (NSIF), transverse stiffness interface (TSIF), and welded contact interface (WCIF), are important factors to consider when studying seismic wave behavior.

The present model may be used in various disciplines, such as high-energy particle physics, earthquake engineering, nuclear fusion, aeronautics, soil dynamics and other areas where memory-dependent derivative and phase delays are significant.

In a variety of technical and geophysical scenarios, wave propagation in an elastic/piezothermoelastic medium with varying magnetic fields, initial stress, temperature, porosity, etc., gives important information regarding the presence of new and modified waves.

This study aims to attempt to construct a new mathematical model of the generalized thermoelasiticity theory based on the memory-dependent derivative (MDD) considering three-phase-lag effects. The governing equations of the problem associated with kernel function and time delay are illustrated in the form of vector matrix differential equations. Implementing Laplace and Fourier transform tools, the problem is sorted out analytically by an eigenvalue approach method. The inversion of Laplace and Fourier transforms are executed, incorporating series expansion procedures. Displacement component, temperature and stress distributions are obtained numerically and illustrated graphically and compared with the existing literature.

This study is to analyze the influence of MDD of three-phase-lag heat conduction interaction in an isotropic semi-infinite medium. The current model has been connected to generalize two-dimensional (2D) thermoelasticity problem. The governing equations are shown in vector matrix form of differential equation concerning Laplace-transformed domain and solved by using the eigenvalue technique. The combined Laplace Fourier transform is applied to find the analytical interpretations of temperature, stresses, displacement for silicon material in a non-dimensional form. Inverse Laplace transform has been found by applying Fourier series expansion techniques introduced by Honig and Hirdes (1984) after performing the inverse Fourier transform.

The main conclusion of this current study is to demonstrate an innovative generalized concept for heat conducting Fourier’s law associated with moderation of time parameter, time delay variable and kernel function by applying the MDDs. However, an important role is played by the time delay parameter to characterize the behavioral patterns of the physical field variables. Further, a new categorization for materials may be created rendering to this new idea along MDD for the time delay variables to develop a new measure of its potential to regulate heat in the medium.

Generalized thermoelasticity is hastily undergoing modification day-by-day from basic thermoelasticity. It has been progressed to get over from the limitations of fundamental thermoelasticity, for instance, infinite velocity components of thermoelasticity interference, in the adequate thermoelastic response of a solid to short laser pulses and deprived illustrations of thermoelastic performance at low temperature. In the past few decades, the fractional calculus is used to change numerous existing models of physical procedure, and its applications are used in various fields of physics, continuum mechanics, fluid mechanics, biology, viscoelasticity, biophysics, signal and image processing, control theory, engineering fields, etc.

The present study discussed wave propagation in a nonlocal generalized thermoelastic half-space with moving an internal heat source under influence of rotation.

Normal mode analysis is introduced to obtain the analytical expressions of the physical quantities.

Numerical results are presented graphically to explore the effects of rotation, the nonlocal parameter, and the time-delay on the physical quantities. It is found that the physical quantities are affected by rotation, the nonlocal parameter, and the time-delay.

The problem is solved based on the classical-coupled theory, the Lord–Shulman theory, and the Green–Lindsay theory with memory-dependent derivative (MDD).

This paper aims to study the variation of energy ratios of different reflected and transmitted waves by calculating the amplitude ratios.

This investigation studied the reflection and transmission of plane waves on an interface of nonlocal orthotropic piezothermoelastic space (NOPHS) and fluid half-space (FHS) in reference to dual-phase-lag theory under three different temperature models, namely, without-two-temperature, classical-two-temperature, and hyperbolic-two-temperature with memory-dependent derivatives (MDDs).

The primary (P) plane waves propagate through FHS and strike at the interface x₃ = 0. The results are one wave reflected in FHS and four waves transmitted in NOPHS. It is noticed that these ratios are observed under the impact of nonlocal, dual-phase-lag (DPL), two-temperature and memory-dependent parameters and are displayed graphically. Some particular cases are also deduced, and the law of conservation of energy across the interface is justified.

According to the available literature, there is no substantial research on the considered model incorporating NOPHS and FHS with hyperbolic two-temperature, DPL and memory.

The current model may be used in various fields, including earthquake engineering, nuclear reactors, high particle accelerators, aeronautics, soil dynamics and so on, where MDDs and conductive temperature play a significant role. Wave propagation in a fluid-piezothermoelastic media with different characteristics such as initial stress, magnetic field, porosity, temperature, etc., provides crucial information about the presence of new and modified waves, which is helpful in a variety of technical and geophysical situations. Experimental seismologists, new material designers and researchers may find this model valuable in revising earthquake estimates.

The researchers may classify the material using the two-temperature parameter and the time-delay operator, where the parameter is a new indication of its capacity to transmit heat in interaction with various materials.

The submitted manuscript is original work done by the team of said authors and each author contributed equally to preparing this manuscript.

In the present paper, the new concept of “memory dependent derivative” in the Pennes’ bioheat transfer and heat-induced mechanical response in human living tissue with variable thermal conductivity and rheological properties of the volume is considered.

A problem of cancerous layered with arbitrary thickness is considered and solved analytically by Kirchhoff and Laplace transformation. The analytical expressions for temperature, displacement and stress are obtained in the Laplace transform domain. The inversion technique for Laplace transforms is carried out using a numerical technique based on Fourier series expansions.

Comparisons are made with the results anticipated through the coupled and generalized theories. The influence of variable thermal, volume materials properties and time-delay parameters for all the regarded fields for different forms of kernel functions is examined.

The results indicate that the thermal conductivity and volume relaxation parameters and MDD parameter play a major role in all considered distributions. This dissertation is an attempt to provide a theoretical thermo-viscoelastic structure to help researchers understand the complex thermo-mechanical processes present in thermal therapies.

This paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.

The analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.

Computational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.

The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.

This investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.

This study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.