The purpose of this research work is to present a numerical study through artificial neural networks (ANNs) to solve a SIQ-based COVID-19 mathematical model using the effects of lockdown. The effects of lockdown are considered to the three-dimensional mathematical model, “susceptible”, “infective” and “quarantined”, i.e. the SIQ system. ANNs and Levenberg–Marquardt backpropagation (LMB) are used to present the numerical analyses of the SIQ system-based COVID-19. Three different types of authentications, testing and training as sample data are applied to solve the SIQ system. Statistical ratios for the SIQ-based COVID-19 mathematical model are selected – 80% for training and 10% for both testing and authentication. The obtained numerical results of the SIQ mathematical system have been compared with the reference dataset, which is constructed through Adams solutions. The obtained numerical performances of the nonlinear SIQ dynamical model are testified with a reduction of the error in mean square sense in the range of 10⁻⁹ to 10⁻¹².

The proposed study demonstrates the flow phenomenon and thermo-variation of a magnetized stretching sheet induced-radiative nanofluid flow. By incorporating the response surface methodology, the heat transfer rate of the thermally convective flow of nanofluid is optimized. The graphene nanomaterial is used in the water-based nanofluid. A dynamic magnetic field, thermal radiation, and the Cattaneo–Christov heat flux model have used to represent the thermal behavior of the nanofluid. The simulation utilizes experimentally estimated values for the nanomaterial’s thermal conductivity and viscosity. To further reveal the thermal enhancement of the flow, the impact of nanoparticle diameter and the solid-liquid interfacial layer is proposed at the molecular level. The response surface methodology and the sensitivity analysis has used to examine the effects of the nanoparticle volume fraction, Biot number, and magnetic parameter on the rate of heat transfer statistically. A set of equations is formed from the governing partial differential equations by implementing suitable similarity transformations. The bvp4c approach is used to solve the problem numerically. The effect of various parameters has displayed through tables, graphs, and surface plots on heat transfer, mass transfer, and the local Nusselt number. It is discovered that as the Biot number increases, so does the concentration and temperature profile. An excellent accord between the present and previously existing solutions is establishing the validity of the achieved results.

Despite the fact the Laplace transform has an appreciable efficiency in solving many equations, it cannot be employed to nonlinear equations of any type. This paper presents a modern technique for employing the Laplace transform LT in solving the nonlinear time-fractional reaction–diffusion model. The new approach is called the Laplace-residual power series method (L-RPSM), which imitates the residual power series method in determining the coefficients of the series solution. The proposed method is also adapted to find an approximate series solution that converges to the exact solution of the nonlinear time-fractional reaction–diffusion equations. In addition, the method has been applied to many examples, and the findings are found to be impressive. Further, the results indicate that the L-RPSM is effective, fast, and easy to reach the exact solution of the equations. Furthermore, several actual and approximate solutions are graphically represented to demonstrate the efficiency and accuracy of the proposed method.

A magneto couple stress nanofluid flow along with double diffusive convection is presented for peristaltic induce flow through symmetric nonuniform channel. A comprehensive mathematical model is scrutinized for couple stress nanofluid magneto nanofluids and corresponding equations of motions are tackled by applying small Reynolds and long wavelength approximation in viewing the scenario of the biological flow. Computational solution is exhibited with the help of graphical illustration for nanoparticle volume fraction, solutal concentration and temperature profiles in MATHEMTICA software. Stream function is also computed numerically by utilizing the analytical expression for nanoparticle volume fraction, solutal concentration and temperature profiles. Whereas pressure gradient profiles are investigated analytically. Impact of various crucial flow parameter on the pressure gradient, pressure rise per wavelength, nanoparticle volume fraction, solutal concentration, temperature and the velocity distribution are exhibited graphically. It has been deduced that temperature profile is significantly rise with Brownian motion, thermophoresis, Dufour effect, also it is revealed that velocity distribution really effected with strong magnetic field and with increasing non-uniformity of the micro channel. The information of current investigation will be instrumental in the development of smart magneto-peristaltic pumps in certain thermal and drug delivery phenomenon.

This paper describes an effective strategy based on Lerch polynomial method for solving mixed integral equations (MIE) in position and time with a strongly symmetric singular kernel in the space $L_2(-1,1)\times C[0,T],(T<1).$ The Quadratic numerical method (QNM) was applied to obtain a system of Fredholm integral equations (SFIE), then the Lerch polynomials method (LPM) was applied to transform SFIE into a system of linear algebraic equations (SLAE). The existence and uniqueness of the integral equation’s solution are discussed using Banach’s fixed point theory. Also, the convergence and stability of the solution and the stability of the error are discussed. Several examples are given to illustrate the applicability of the presented method. The Maple program obtains all the results. A numerical simulation is carried out to determine the efficacy of the methodology, and the results are given in symmetrical forms. From the numerical results, it is noted that there is a symmetry utterly identical to the kernel used when replacing each x with y.

The present computational model is built to analyze the energy and mass transition rate through a copper and cobalt ferrite water-based hybrid nanofluid (hnf) flow caused by the fluctuating wavy spinning disk. Cobalt ferrite (CoFe₂O₄) and copper (Cu) nanoparticles (nps) are incredibly renowned in engineering and technological research due to their vast potential applications in nano/microscale structures, devices, materials, and systems related to micro- and nanotechnology. The flow mechanism has been formulated in the form of a nonlinear set of PDEs. That set of PDEs has been further reduced to the system of ODEs through resemblance replacements and computationally solved through the parametric continuation method. The outcomes are verified with the Matlab program bvp4c, for accuracy purposes. The statistical outputs and graphical evaluation of physical factors versus velocity, energy, and mass outlines are given through tables and figures. The configuration of a circulating disk affects the energy transformation and velocity distribution desirably. In comparison to a uniform interface, the uneven spinning surface augments energy communication by up to 15%. The addition of nanostructured materials (cobalt ferrite and copper) dramatically improves the solvent physiochemical characteristics. Furthermore, the upward and downward oscillation of the rotating disc also enhances the velocity and energy distribution.