Recently,Yu et al.(2014)proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative.The magneto-thermoelastic responses in a perfectly conducting thermoelastic so...Recently,Yu et al.(2014)proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative.The magneto-thermoelastic responses in a perfectly conducting thermoelastic solid half-space is investigated in the context of the above new theory.Normal mode analysis together with an eigenvalue expansion technique is used to solve the resulting non-dimensional coupled governing equations.The obtained solutions are then applied to a specific problem for thermoelastic half-space whose boundary is subjected to a time-dependent thermal shock and zero stress.The effects of the kernel function,time-delay parameter,magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically.The results show that these parameters has significant influence on the variations of the considered variables.展开更多
The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat con...The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.展开更多
Hepatitis B virus (HBV) remains a persistent global health concern, with recent research advancing our understanding of its transmission dynamics and potential interventions.The present study proposes a mathematical m...Hepatitis B virus (HBV) remains a persistent global health concern, with recent research advancing our understanding of its transmission dynamics and potential interventions.The present study proposes a mathematical model of Hepatitis B Virus (HBV) epidemics using fractional calculus, with a special emphasis on the influence of spontaneous clearance across diverse population groups. Using the Atangana-Baleanu derivative, the model accounts for the complications of vertical and horizontal transmission, therapy, immunisation, and spontaneous clearance. Numerical simulations with different fractional orders demonstrate how spontaneous clearance affects the dynamics of susceptible, chronic, treated, and recovered populations. The findings indicate that in vulnerable populations, increasing spontaneous clearance reduces vulnerability because people either clear the illness naturally or gain resistance.However, in chronic populations, spontaneous clearance is insufficient for complete recovery without treatment. The combination of therapy and spontaneous clearance improves the treated population, demonstrating the beneficial effects of both medical intervention and natural immunity. Furthermore, increased spontaneous clearance boosts the restored population, demonstrating the immune system's ability to eliminate the virus over time. The fractional-order framework captures the memory effect of illness development, revealing how healing is time-dependent and how immune responses have a long-term impact. This study emphasises the need of combining spontaneous clearance with medical therapies to improve HBV management and public health consequences. Hepatitis B virus (HBV) remains a persistent global health concern, with recent research advancing our understanding of its transmission dynamics and potential interventions. This study presents a fractional mathematical model of HBV infection, employing the Atangana-Baleanu derivative with Mittag-Leffler kernels to capture memory-dependent and nonlocal transmission processes. The model integrates vertical and horizontal transmission pathways, treatment strategies, immunization efforts, and spontaneous clearance, providing a nuanced perspective compared to classical models. Stability conditions are analyzed through fixed-point theory, revealing the global stability of both disease-free and endemic states under specific values of the basic reproduction number R0. Numerical simulations demonstrate the model's effectiveness in capturing the complex dynamics of HBV, with fractional-order parameters enhancing prediction accuracy. This approach offers valuable insights into optimizing public health interventions and treatment strategies for managing HBV infections effectively.展开更多
The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elastici...The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.展开更多
文摘Recently,Yu et al.(2014)proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative.The magneto-thermoelastic responses in a perfectly conducting thermoelastic solid half-space is investigated in the context of the above new theory.Normal mode analysis together with an eigenvalue expansion technique is used to solve the resulting non-dimensional coupled governing equations.The obtained solutions are then applied to a specific problem for thermoelastic half-space whose boundary is subjected to a time-dependent thermal shock and zero stress.The effects of the kernel function,time-delay parameter,magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically.The results show that these parameters has significant influence on the variations of the considered variables.
文摘The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.
文摘Hepatitis B virus (HBV) remains a persistent global health concern, with recent research advancing our understanding of its transmission dynamics and potential interventions.The present study proposes a mathematical model of Hepatitis B Virus (HBV) epidemics using fractional calculus, with a special emphasis on the influence of spontaneous clearance across diverse population groups. Using the Atangana-Baleanu derivative, the model accounts for the complications of vertical and horizontal transmission, therapy, immunisation, and spontaneous clearance. Numerical simulations with different fractional orders demonstrate how spontaneous clearance affects the dynamics of susceptible, chronic, treated, and recovered populations. The findings indicate that in vulnerable populations, increasing spontaneous clearance reduces vulnerability because people either clear the illness naturally or gain resistance.However, in chronic populations, spontaneous clearance is insufficient for complete recovery without treatment. The combination of therapy and spontaneous clearance improves the treated population, demonstrating the beneficial effects of both medical intervention and natural immunity. Furthermore, increased spontaneous clearance boosts the restored population, demonstrating the immune system's ability to eliminate the virus over time. The fractional-order framework captures the memory effect of illness development, revealing how healing is time-dependent and how immune responses have a long-term impact. This study emphasises the need of combining spontaneous clearance with medical therapies to improve HBV management and public health consequences. Hepatitis B virus (HBV) remains a persistent global health concern, with recent research advancing our understanding of its transmission dynamics and potential interventions. This study presents a fractional mathematical model of HBV infection, employing the Atangana-Baleanu derivative with Mittag-Leffler kernels to capture memory-dependent and nonlocal transmission processes. The model integrates vertical and horizontal transmission pathways, treatment strategies, immunization efforts, and spontaneous clearance, providing a nuanced perspective compared to classical models. Stability conditions are analyzed through fixed-point theory, revealing the global stability of both disease-free and endemic states under specific values of the basic reproduction number R0. Numerical simulations demonstrate the model's effectiveness in capturing the complex dynamics of HBV, with fractional-order parameters enhancing prediction accuracy. This approach offers valuable insights into optimizing public health interventions and treatment strategies for managing HBV infections effectively.
文摘The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.
