In this paper, we proposed a sustainable inventory model with a learning effect for imperfect quality items under different kinds of fuzzy environments like crisp, general fuzzy, cloudy fuzzy, and monsoon fuzzy. We divided the mathematical model into three parts under the learning effect according to the real-time fuzzy components (crisp, cloudy, and monsoon environments) of the demand rate of the items. We minimized the total inventory cost with respect to cycle length in each environment under the proposed assumptions. The non-linear optimization technique is applied for the algorithm and the solution method to find the decision variable. Finally, we compared the total inventory cost under different fuzzy environments and our finding is that the fuzzy monsoon environment is a more effective fuzzy environment than crisp and cloudy fuzzy environments. We have presented a numerical example for the validation of the proposed model and have shown the impact of the inventory input parameters on the cycle length and total inventory fuzzy cost. The managerial insights and future scope of this proposed study have been shown in the sensitivity analysis and conclusion. The limitations, application, future extension and scope, and social implementation have been shown in this research study.

In the present scenario, the whole world struggling with COVID-19 which affects highly transmittable and pathogenic viral infection that rose by a newly discovered coronavirus and believed to be originated in China. The more serious effects of the virus occur for the people who are under medical problems as diabetes, chronic respiratory diseases, cancer, and cardiovascular diseases also in older persons. Because of the unavailability of proper vaccine, medical facility and medical experts the current situation becomes worst and uncontrollable for many countries. Hence, in order to overcome and reduce the spread of infection there is a necessity to prepare the predictive mathematical model due to prevention factor and suitability conditions. Enlightened by the coronavirus, the present study deals with a novel mathematical model of COVID-19 to investigate the impact of S-I-R-M model due to the influence of prevention factor and suitability conditions. Numerical calculation for infectious rate, recovery rate and mortality rate have been discussed and displayed graphically. Moreover, some comparisons have been shown in figure to estimate the effect of prevention factor.

Purpose: The purpose of the paper is to prepare the hygrothermal model with fraction order theory in a mathematical aspect.Design/methodology/approach: In this study, linear hygrothermoelastic theory is adopted to analyze and discuss the memory effect in a finite length hollow cylinder subjected to hygrothermal loading.Findings: Analytical solutions of temperature, moisture and stresses are obtained in this study by using the decoupling technique and the method of Integral transform.Originality/value: The paper deals with the original work based on hygrothermal response in hollow cylinder by theory of uncoupled-coupled heat and moisture.

In this paper, a hollow circular cylinder of finite length with finite extent occupying the space $D:a\le r\le b,0\le z\le h$ is considered. Based on the hygrothermoelasticity theory, the transient response of a hollow circular cylinder subjected to the hygrothermal loading at the surface is analyzed. The analytical solution for the coupling and uncoupling effects of temperature, moisture, and thermal stresses is obtained by using the integral transform technique. The numerical results of the transient response of the hygrothermoelasticity field are presented graphically for a graphite fiber–reinforced epoxy matrix composite material (T300/5208).

Memory-dependent derivatives (MDD) have physical meaning, and compared to fractional derivatives, they are more suitable and convenient for temporal remodeling. In this study, the temperature and stress distributions in an infinitely extended generalized thermally elastic solid circular cylinder have been investigated by utilizing the concept of a memory-dependent heat conduction model. The homogeneous, isotropic, infinitely long solid circular cylinder is considered to have a lateral surface that is free of traction and is subjected to a known surrounding temperature. In the domain of the integral Laplace transform, the problem is worked out, and its complex inversion is performed numerically using the Fourier series expansion method. The material properties of copper metal are chosen for the purpose of numerical computation, and the thermoelastic impact of time delay on temperature distribution, displacement distribution, and thermal stresses are represented graphically. Also, time delay's effect on temperature history, displacement history, and thermal heat transfer stress history are shown, respectively. This study could also benefit mathematicians and researchers involved in the development of thermoelasticity, as it accounts for the memory-related derivatives that are useful in explaining the behaviour of a variety of physical processes. The thermal fluctuations captured by various factors with memory-dependent responses are used in engineering applications to realistically design machines or structures.

In this paper, analytical solutions are presented for temperature and thermal behavior of a thermosensitive multilayered annular disc due to point heat source. Convective heating is applied to both the innermost and outermost layers. The nonlinearity of the thermal diffusivity equation is dealt...