Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations.

In this paper, firstly, the " Haar wavelet method " is used to give approximate solutions for coupled systems of linear fractional Fredholm integro-differential equations. Moreover, we consider the fractional derivative to be described in the Caputo sense. The general idea of this technique is simply based on reducing this kinds of coupled systems into systems of algebraic equations which are easily to deal with and solve. Also, Laplace transform operator is included to develop a sophisticated approach which we called " Laplace Haar wavelet method " as an adjustment to " Haar wavelet method " to reduce the error and computational time. We provide illustrative examples to confirm validity, efficiency, accuracy, and applicability of the proposed methods.

Free convective oscillatory flow due to inclined perpendicular shield subject to the thermos-diffusion and suction effects.

An unsteady free convective flow of an electrically conducting viscous fluid due to accelerated inestimable inclined perpendicular shield has been presented in presence of heat and mass transfer phenomenon. The applications of thermos-diffusion and heat source are also incorporated. The chemical reaction consequences are considered in the concentration equation. The compelling meadow is considered to be homogeneous and practical perpendicular to the flow direction. Further, the oscillatory suction effects are also taken into observations for porous regime. The closed form expressions are resulted with implementation of perturbation approach. The non-dimensional expression for the proposed governing system is yield out with entertaining appropriate variables. The graphically influence of parameters is studied. Following to obtained observations, it is claimed that declining deviation in velocity is predicted with chemical reactive factor. Further, less thermal transport between container to fluid is noticed for radiative absorption parameter.

On the Bioconvective Aspect of Viscoelastic Micropolar Nanofluid Referring to Variable Thermal Conductivity and Thermo-Diffusion Characteristics.

The bioconvective flow of non-Newtonian fluid induced by a stretched surface under the aspects of combined magnetic and porous medium effects is the main focus of the current investigation. Unlike traditional aspects, here the viscoelastic behavior has been examined by a combination of both micropolar and second grade fluid. Further thermophoresis, Brownian motion and thermodiffusion aspects, along with variable thermal conductivity, have also been utilized for the boundary process. The solution of the nonlinear fundamental flow problem is figured out via convergent approach via Mathematica software. It is noted that this flow model is based on theoretical flow assumptions instead of any experimental data. The efficiency of the simulated solution has been determined by comparing with previously reported results. The engineering parameters' effects are computationally evaluated for some definite range.

Thermal transport of biological base fluid with copper and iron oxide nanoparticles in wavy channel.

The nanoparticles are frequently used in biomedical science for the treatment of diseases like cancer and these nanoparticles are injected in blood which is transported in the cardiovascular system on the principle of peristalsis. This study elaborates the effects of Lorentz force and joule heating on the peristaltic flow of copper and iron oxide suspended blood based nanofluid in a complex wavy non-uniform curved channel. The Brinkman model is utilized for the temperature dependent viscosity and thermal conductivity. The problem is formulated using the fundamental laws in terms of coupled partial differential equations which are simplified using the creeping flow phenomenon. The graphical results for velocity, temperature, streamlines, and axial pressure are simulated numerically. The concluded observations deduce that the solid volume fraction of nanoparticles reduces the velocity and enhance the pressure gradient and accumulation of trapping bolus in the upper half of the curved channel is noticed for temperature dependent viscosity.

Darcy resistance flow of Sutterby nanofluid with microorganisms with applications of nano-biofuel cells.

The objective of current research is to endorse the thermal aspect of Sutterby nanofluid containing the microorganisms due the stretched cylinder. The features of nonlinear thermal radiation, Darcy resistance and activation energy are also incorporated to inspect the thermal prospective. The problem is further extended with implementation of modified Fourier and Fick's theories. The results are presented for the stretched cylinder and also for stationary plate. The numerical formulation for the problem is presented by following the shooting technique. The comparative numerical is performed to verify the computed simulations. The results convey that the presence of Darcy resistance parameter enhanced the velocity more effectively for stretched cylinder. A reduction in velocity due to Sutterby fluid parameter and buoyancy ratio parameter has been observed. Moreover, the temperature profile enhanced with larger sponginess parameter more effectively for stretching cylinder.

Bioconvection flow in accelerated couple stress nanoparticles with activation energy: bio-fuel applications.

On the account of significance of bioconvection in biotechnology and several biological systems, valuable contributions have been performed by scientists in current decade. In current framework, a theoretical bioconvection model is constituted to examine the analyzed the thermally developed magnetized couple stress nanoparticles flow by involving narrative flow characteristics namely activation energy, chemical reaction and radiation features. The accelerated flow is organized on the periodically porous stretched configuration. The heat performances are evaluated via famous Buongiorno's model which successfully reflects the important features of thermophoretic and Brownian motion. The composed fluid model is based on the governing equations of momentum, energy, nanoparticles concentration and motile microorganisms. The dimensionless problem has been solved analytically via homotopic procedure where the convergence of results is carefully examined. The interesting graphical description for the distribution of velocity, heat transfer of nanoparticles, concentration pattern and gyrotactic microorganism significance are presented with relevant physical significance. The variation in wall shear stress is also graphically underlined which shows an interesting periodic oscillation near the flow domain. The numerical interpretation for examining the heat mass and motile density transfer rate is presented in tubular form.

Finite difference simulations for non-isothermal hydromagnetic peristaltic flow of a bio-fluid in a curved channel: Applications to physiological systems.

Owing to the fundamental significances of peristalsis phenomenon in various biological systems like circulation of blood in vessels, lungs devices, pumping of blood in heart and movement of chyme in the gastrointestinal tract, variety of research by scientist on this topic has been presented in recently years. The peristaltic pumping plays a novel role in various industrial processes like transfer of sanitary materials, the pumping equipment design of roller pumps and many more. The present article investigates numerically the theoretical aspects of heat and mass transportation in peristaltic pattern of Carreau fluid through a curved channel. The computations for axial velocity, pressure rise, temperature field, mass concentration, and stream function are carried out under low Reynolds number and long wavelength approximation in the wave frame of reference by utilizing appropriate numerical implicit finite difference technique (FDM). The implementation of numerical procedure and graphical representation of the computations are accomplished using MATLAB language. The impacts of rheological parameters of Carreau fluid, Brinkmann number, curvature parameter and Hartmann number are shown and discussed briefly. The study shows that for shear thinning of bio-materials, the velocity exhibits the boundary layer character near the boundary walls for greater Hartmann number. The interesting observations based on numerical simulations are graphically elaborated. The results show that the curvature of channel with larger value allows more heat transportation within the flow domain. On the contrary, inside the channel wall, the solutal mass concentration follows an increasing trend with decreasing the channel curvature. The temperature profile enhanced with increment of power-law index and curvature parameter. Moreover, the concentration profile increases with Brinkmann number and Hartmann number.

Chemically reactive bioconvection flow of tangent hyperbolic nanoliquid with gyrotactic microorganisms and nonlinear thermal radiation.

On the account of motivating fabrication of bioconvection phenomenon in various engineering and industrial systems, an attention has been devoted by researchers in current decade. Therefore, this theoretical investigation deals with the utilization of bioconvection phenomenon in flow of tangent hyperbolic nanofluid over an accelerated moving surface. It is assumed that the flow is generated due to periodically motion of the sheet. The energy equation is modified by entertaining the nonlinear thermal radiation features. The chemical reaction effects are elaborated in the concentration equation. Moreover, the significance of present flow problem increases by utilizing the thermophoresis and Brownian motion effects. The governing equations are transmuted into non-dimensional form with utilization of appropriate quantities. The analytical solution is computed by using homotopy analysis method. The implications of promising parameters on velocity profile, temperature profile, nanoparticles volume fraction and microorganisms profile is evaluated graphically. The presence of radiation parameter, thermophoresis and Brownian motion effects are more frequent for enhancement of heat transfer. The reported observations can efficiently use in the improvement of heat transfer devices as well as microbial fuel cells.

Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials.

In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5-6): 579-588, 2000), while others agrees with Pottinger's results (Pottinger in Z Agnew Math Mech 56: T310-T311, 1976).

A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector.

In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector.

The effect of nanoparticles on plankton dynamics: a mathematical model.

A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.