Analysis of novel fractional COVID-19 model with real-life data application.

The current work is of interest to introduce a detailed analysis of the novel fractional COVID-19 model. Non-local fractional operators are one of the most efficient tools in order to understand the dynamics of the disease spread. For this purpose, we intend as an attempt at investigating the fractional COVID-19 model through Caputo operator with order χ ∈ ( 0 , 1 ) . Employing the fixed point theorem, it is shown that the solutions of the proposed fractional model are determined to satisfy the existence and uniqueness conditions under the Caputo derivative. On the other hand, its iterative solutions are indicated by making use of the Laplace transform of the Caputo fractional operator. Also, we establish the stability criteria for the fractional COVID-19 model via the fixed point theorem. The invariant region in which all solutions of the fractional model under investigation are positive is determined as the non-negative hyperoctant R + 7 . Moreover, we perform the parameter estimation of the COVID-19 model by utilizing the non-linear least squares curve fitting method. The sensitivity analysis of the basic reproduction number R 0 c is carried out to determine the effects of the proposed fractional model's parameters on the spread of the disease. Numerical simulations show that all results are in good agreement with real data and all theoretical calculations about the disease.

Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator.

This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant S. aureus (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant S. aureus (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both R 0 H and R 0 C are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order α .

Modeling of pressure-volume controlled artificial respiration with local derivatives.

We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.

Fractional models with singular and non-singular kernels for energy efficient buildings.

In the current study, we investigate and analyze the fractional version of the heating and cooling model for buildings with energy efficiency. We apply the Caputo fractional derivative, Caputo-Fabrizio, and Atangana-Baleanu in the Caputo sense in the analysis and investigation of the governing model. We derive some novel analytical solutions by means of Laplace's transform. Simulation analysis is carried out in order to shed more light on the physical features of the governing models. To believe the results obtained, the fractional order has been allowed to vary between (0,1], whereupon the physical observations match those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional derivatives.