Analytical solution for the dynamics and optimization of fractional Klein-Gordon equation: an application to quantum particle.

Klein-Gordon equation characterizes spin-particles through neutral charge field within quantum particle. In this context, fractionalized Klein-Gordon equation is investigated for the comparative analysis of the newly presented fractional differential techniques with non-singularity among kernels. The non-singular and non-local kernels of fractional differentiations have been employed on Klein-Gordon equation for the development of governing equation. The analytical solutions of Klein-Gordon equation have been traced out by fractional techniques by means of Laplace transforms and expressed in terms of series form and gamma function. The data analysis of fractionalized Klein-Gordon equation is observed for Pearson's correlation coefficient, probable error and regression analysis. For the sake of comparative analysis of fractional techniques, 2D sketch, 3D pie chart, contour surface with projection and 3D bar sketch have been depicted on the basis of embedded parameters. Our results suggest that varying frequency has reversal trends for quantum wave and de Broglie wave.

Role of copper and alumina for heat transfer in hybrid nanofluid by using Fourier sine transform.

The convection, thermal conductivity, and heat transfer of hybrid nanofluid through nanoparticles has become integral part of several natural and industrial processes. In this manuscript, a new fractionalized model based on hybrid nanofluid is proposed and investigated by employing singular verses and non-singular kernels. The mathematical modeling of hybrid nanofluid is handled via modern fractional definitions of differentiations. The combined Laplace and Fourier Sine transforms have been configurated on the governing equations of hybrid nanofluid. The analytical expression of the governing temperature and velocity equations of hybrid nanofluid have been solved via special functions. For the sake of thermal performance, dimensional analysis of governing equations and suitable boundary conditions based on Mittage-Leffler function have been invoked for the first time in literature. The comparative analysis of heat transfer from hybrid nanofluid has been observed through Caputo-Fabrizio and Atangana-Baleanu differential operators. Finally, our results suggest that volume fraction has the decelerated and accelerated trends of temperature distribution and inclined and declined profile of heat transfer is observed copper and alumina nanoparticles.

Thermal characteristics of longitudinal fin with Fourier and non-Fourier heat transfer by Fourier sine transforms.

The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.

Role of pine wilt disease based on optimal control strategy at multiple scales: A case study of Korea.

Pine wilt disease is one of the most serious conifer diseases: this is because pine trees contribute greatly to the economy and domestic wealth in Korea. Our model of this disease is based on the parametrisation of infectious pine trees in Korea for the period of 2010-2019. The model captures the growth in case onsets and the estimated results are almost compatible with the reported data. To control the spread of this disease to the whole pine tree community, we found a threshold parameter called 'basic reproduction number' using the nextgeneration matrix method. During the analysis of the model, equilibrium points were first computed: there are two points -one has no disease class and other has all the disease classes. For the global behaviour of the mathematical model of these two points, Lypunove functional theory was used for disease-free and endemic equilibrium. Sensitivity analysis was performed to observe the relative importance of these parameters to the transmission and prevalence of pine wilt disease. To control the dissemination of the disease, we formulated an optimal control problem. Strategies used to control this disease were based on the consequences of the significant effects of the estimated parameters on the basic reproduction number. We re-examined the mathematical system to determine the agreement between numerically and analytically calculated outcomes. After analysing the problem numerically, we can discern that the numerical findings support the results calculated analytically.

A Mathematical and Statistical Estimation of Potential Transmission and Severity of COVID-19: A Combined Study of Romania and Pakistan.

During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets, and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time to reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed.