Mathematical model for the novel coronavirus (2019-nCOV) with clinical data using fractional operator.

Coronavirus infection (COVID-19) is a considerably dangerous disease with a high demise rate around the world. There is no known vaccination or medicine until our time because the unknown aspects of the virus are more significant than our theoretical and experimental knowledge. One of the most effective strategies for comprehending and controlling the spread of this epidemic is to model it using a powerful mathematical model. However, mathematical modeling with a fractional operator can provide explanations for the disease's possibility and severity. Accordingly, basic information will be provided to identify the kind of measure and intrusion that will be required to control the disease's progress. In this study, we propose using a fractional-order SEIARPQ model with the Caputo sense to model the coronavirus (COVID-19) pandemic, which has never been done before in the literature. The stability analysis, existence, uniqueness theorems, and numerical solutions of such a model are displayed. All results were numerically simulated using MATLAB programming. The current study supports the applicability and influence of fractional operators on real-world problems.

Spectral shifted Chebyshev collocation technique with residual power series algorithm for time fractional problems.

In this paper, two problems involving nonlinear time fractional hyperbolic partial differential equations (PDEs) and time fractional pseudo hyperbolic PDEs with nonlocal conditions are presented. Collocation technique for shifted Chebyshev of the second kind with residual power series algorithm (CTSCSK-RPSA) is the main method for solving these problems. Moreover, error analysis theory is provided in detail. Numerical solutions provided using CTSCSK-RPSA are compared with existing techniques in literature. CTSCSK-RPSA is accurate, simple and convenient method for obtaining solutions of linear and nonlinear physical and engineering problems.

Adapting Laplace residual power series approach to the Caudrey Dodd Gibbon equation.

In real-life applications, nonlinear differential equations play an essential role in representing many phenomena. One well-known nonlinear differential equation that helps describe and explain many chemicals, physical, and biological processes is the Caudrey Dodd Gibbon equation (CDGE). In this paper, we propose the Laplace residual power series method to solve fractional CDGE. The use of terms that involve fractional derivatives leads to a higher degree of freedom, making them more realistic than those equations that involve the derivation of an integer order. The proposed method gives an easy and faster solution in the form of fast convergence. Using the limit theorem of evaluation, the experimental part presents the results and graphs obtained at several values of the fractional derivative order.

Radiative flow of non Newtonian nanofluids within inclined porous enclosures with time fractional derivative.

An unsteady convection-radiation interaction flow of power-law non-Newtonian nanofluids using the time-fractional derivative is examined. The flow domain is an enclosure that has a free surface located at the top boundaries. Also, the geometry is filled by aluminum foam as a porous medium and the overall thermal conductivity as well as the heat capacity are approximated using a linear combination of the properties of the fluid and porous phases. Additionally, the dynamic viscosity and thermal conductivity of the mixture are expressed as a function of velocity gradients with a fractional power. Marangoni influences are imposed to the top free surface while the bottom boundaries are partially heated. Steps of the solution methodology are consisting of approximation of the time fractional derivatives using the conformable definition, using the finite differences method to discretize the governing system and implementation the resulting algebraic system. The main outcomes reveled that as the fractional order approaches to one, the maximum values of the stream function, the bulk-averaged temperature and cup-mixing temperature are reduces, regardless values of the time.