On some fixed point results using CG simulation functions via w-distance with applications.

Based on the notion of class of CG simulation functions, we launch the concept of (ρ,ϑ)-ZG-contraction on the setting of w-distance mappings. We employ our new concept to formulate and prove several fixed point results over the complete metric spaces. Also, we provide some concrete examples to show the usability of the obtained results. Furthermore, we study the existence of a unique solution of nonlinear fractional differential equations, nonlinear integral equations and spring-mass system problems. The results presented in this manuscript generalize many of the results known in the literature.

Unsteady micropolar nanofluid flow past a variable riga stretchable surface with variable thermal conductivity.

In this study, we considered the flow of a micropolar fluid over a vertical Riga sheet. The non linear stretching sheet is considered. The effects of variable thermal conductivity and radiation on the Riga sheet are taken into account. Additionally, we also debated the Brownian motion and thermophoretic. To simplify the partial differential equations, we converted them into dimensionless ordinary differential equations using suitable similarity variables and solved dimensionless system numerically using the bvp4c function. The impact of some intended parameters on the dimensionless velocity, microrotation, temperature, and concentration distributions graphically are presented and the numerical outcomes of physical quantities like skin friction, Nusselt number, Sherwood number, and couple stress have been presented in tabular form. The micropolar parameter increased which increased the couple stress and friction at surface. Because, the fluid rotation increased which increased friction at surface and also increased the couple stress. The transfer of mass decayed and transfer of heat heightened by larger values of variable thermal conductivity. Thermal conductivity improved which improved the heat transfer phenomena, so transfer of heat at surface becomes larger while also reducing the transfer of mass.

Predicting the strengths of date fiber reinforced concrete subjected to elevated temperature using artificial neural network, and Weibull distribution.

Date palm fiber (DPF) is normally used as fiber material in concrete. Though its addition to concrete leads to decline in durability and mechanical strengths performance. Additionally, due to its high ligno-cellulose content and organic nature, when used in concrete for high temperature application, the DPF can easily degrade causing reduction in strength and increase in weight loss. To reduce these effects, the DPF is treated using alkaline solutions. Furthermore, pozzolanic materials are normally added to the DPF composites to reduce the effects of the ligno-cellulose content. Therefore, in this study silica fume was used as supplementary cementitious material in DPF reinforced concrete (DPFRC) to reduce the negative effects of elevated temperature. Hence this study aimed at predicting the residual strengths of DPFRC enhanced/improved with silica fume subjected to elevated temperature using different models such as artificial neural network (ANN), multi-variable regression analysis (MRA) and Weibull distribution. The DPFRC is produced by adding DPF in proportions of 0%, 1%, 2% and 3% by mass. Silica fume was used as partial substitute to cement in dosages of 0%, 5%, 10% and 15% by volume. The DPFRC was then subjected to elevated temperatures between 200 and 800 °C. The weight loss, residual compressive strength and relative strengths were measured. The residual compressive strength and relative strength of the DPFRC declined with addition of DPF at any temperature. Silica fume enhanced the residual and relative strengths of the DPFRC when heated to a temperature up to 400 °C. To forecast residual compressive strength (RCS) and relative strength (RS), we provide two distinct ANN models. The first layer's inputs include DPF (%), silica fume (%), temperature (°C), and weight loss (%). The hidden layer is thought to have ten neurons. M-I is the scenario in which we use RCS as an output, whereas M-II is the scenario in which we use RS as an output. The ANN models were trained using the Levenberg-Marquardt backpropagation algorithm (LMBA). Both neural networking models exhibit a significant correlation between the predicted and actual values, as seen by their respective R = 0.99462 and R = 0.98917. The constructed neural models M-I and M-II are highly accurate at predicting RCS and RS values. MRA and Weibull distribution were used for prediction of the strengths of the DPFRC under high temperature. The developed MRA was found to have a good prediction accuracy. The residual compressive strength and relative strength followed the two-parameter Weibull distribution.

Thermodynamic flow of radiative induced magneto modified Maxwell Sutterby fluid model at stretching sheet/cylinder.

A steady flow of Maxwell Sutterby fluid is considered over a stretchable cylinder. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied on the fluid flow. Joule heating and radiation impacts are studied under the temperature-dependent properties of the liquid. Having the above assumptions, the mathematical model has been evolving via differential equations. The differential equations are renovated in the dimensionless form of ordinary differential equations using the appropriate transformations. The numerical results have been developed employing numerical techniques on the ordinary differential equations. The impact of involving physical factors on velocity, induced magneto hydrodynamic, and temperature function is debated in graphical and tabular form. The velocity profile is boosted by thicker momentum boundary layers, which are caused by higher values of the magnetic field factor. So, the fluid flow becomes higher velocity due to enlarging values of the magnetic field factor. Heat transfer factor and friction at surface factor boosted up for increment of [Formula: see text] (Magnetic field factor). The [Formula: see text](Magnetic field factor) is larger which better-quality of heat transfer at surface and also offered the results of friction factor boosting up in both cases of stretching sheet/cylinder. The [Formula: see text](Magnetic Prandtl number) increased which provided better-quality of heat transfer at surface.

Heat and mass transfer of generalized fourier and Fick's law for second-grade fluid flow at slendering vertical Riga sheet.

In this analysis, the generalized Fourier and Fick's law for Second-grade fluid flow at a slendering vertical Riga sheet is examined along with thermophoresis and Brownian motion effects. Boundary layer approximations in terms of PDE's (Partial Differential Equations) are used to build the mathematical model. An appropriate transformation has been developed by using the Lie symmetry method. PDE's (Partial Differential Equations) are transformed into ODE's (Ordinary Differential Equations) by implementing the suitable transformation. A numerical method called bvp4c is used to explain the dimensionless system (ODE's). Graphs and tables are used to interpret the impact of the significant physical parameters. The curves of temperature function declined due to enchanting the values of the thermophoresis Parameter. The temperature is produced at a low level due to enchanting the values of thermophoresis because this force transports burn at a low 10 µm diameter so the temperature becomes lessor. Increments of thermophoresis parameter which enhanced the values of concentration Function. As the concentration boundary layer increased which declined the mass transfer due increment in thermophoresis. The curves of temperature function are increasing due to enhancing the values of the Brownian parameter because addition in the Brownian motion, improved the movement of particles ultimately increasing the kinematic energy of fluid which improved the heat transfer phenomena. Increments of Brownian parameter which declined the values of concentration function. Physically, the kinematic energy improved which declined the mass transfer rate near the surface.

Transportation of nanomaterial Maxwell fluid flow with thermal slip under the effect of Soret-Dufour and second-order slips: nonlinear stretching.

In this study, impact of second order slip for Maxwell fluid at vertical exponential stretching sheet is deliberated. Dufour and Soret impact for vertical exponential stretching sheet under nonlinear radiation are deliberated. Thermal and concentration slips with viscous dissipation are taken into account under the Buongiorno's model. Under the above assumptions, the differential model constructed using the boundary layer approximations using the governing equations. The similarities transformations are introduced which applied the differential model (partial differential equations) and developed the dimensionless differential equations (ordinary differential equations). The dimensionless differential equations are cracked by numerical scheme. The impact of physical parameters are presented by tables and graphs. The curves of fluid velocity enhanced due to increasing the values of velocity slip. Velocity slip is a fluid-boundary interaction in physics. If the velocity slip increased, the fluid velocity profile would eventually become increasing. Temperature curves declined by improving values of [Formula: see text]. The thermal thickness reduced when improved the values of [Formula: see text].

FENE-P fluid flow generated by self-propelling bacteria with slip effects.

It is hypothesized that gliding bacteria move by producing waves on their own surface and leave an adhesive slime trail. Slime is basically a viscoelastic slippery material. Based on these observations, we use a mathematical model (of undulating sheet) to examine the locomotion of gliding bacteria over a layer of non-Newtonian slime. The constitutive equations of FENE-P model are employed to characterize the rheological behavior of the non-Newtonian slime. Moreover, substratum beneath the slime is approximated by a multi-sinusoidal sheet. A hybrid computational technique to solve the second order DE with a system of algebraic equations is presented. The speed of organism, flow rate and energy loss at larger values of the involved parameters are simulated using bvp5c in conjunction with a modified Newton-Raphson technique (MNRT). The comparison of soft and rigid substrate, slip and no-slip boundary conditions, Newtonian and non-Newtonian slime is displayed in several figures. Streamlines pattern and velocity of the slime are also drawn for the realistic pairs of speed and flow rate and are thoroughly explained.

Darcy resistant of Soret and Dufour impact of radiative induced magnetic field sutterby fluid flow over stretching cylinder.

The incompressible two-dimensional steady flow of Sutterby fluid over a stretching cylinder is taken into account. The magnetic Reynolds number is not deliberated low in the present analysis. Radiation and variable thermal conductivity are considered to debate the impact on the cylindrical surface. The Dufour and Soret impacts are considered on the cylinder. The mathematical model is settled by employing boundary layer approximations in the form of differential equations. The system of differential equations becomes dimensionless using suitable transformations. The dimensionless nonlinear differential equations are solved through a numerical scheme(bvp4c technique). The flow parameters of physical effects on the velocity, temperature, heat transfer rate, and friction between surface and liquid are presented in tabular as well as graphical form. The velocity function declined by improving the values of the Sponginess parameter. The fluid temperature is reduced by increment in curvature parameter.

An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model.

An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme's stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

Design of nonstandard computational method for stochastic susceptible-infected-treated-recovered dynamics of coronavirus model.

The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard computational numerical methods for the solution of the stochastic system. The design of a nonstandard computation method for the stochastic system is innovative. Unfortunately, standard computation numerical methods are time-dependent and violate the structure properties of models, such as positivity, boundedness, and dynamical consistency of the stochastic system. To that end, convergence analysis of nonstandard computational methods and simulation with a comparison of standard computational methods are presented.