In this paper, we study certain interesting and useful properties of incomplete
ℵ‐functions. The incomplete
ℵ‐function is an extension of the
ℵ‐function. We find several useful classical integral ...transforms of these functions. Further, we examine the fractional calculus with the incomplete
ℵ‐functions and point out several special cases. Finally, we give the applications of incomplete
ℵ‐functions in detecting glucose supply in human blood.
Our main objective in the present work is to elaborate the characteristics of heat transport and magneto-hydrodynamics (MHD) finite film flow of human blood with Carbon Nanotubes (CNTs) nanofluids ...over a stretchable upright cylinder. Two kinds of CNTs nanoparticles, namely (i) SWCNTs (single walled carbon nanotubes) and (ii) MWCNTs (multi walled carbon nanotubes), are used with human blood as a base liquid. In addition, a uniform magnetic field (B) has been conducted perpendicularly to the motion of nanoliquid. The transformation of the partial differential structure into a non-linear ordinary differential structure is made by using appropriate dimensionless quantities. The controlling approach of the Homotopy analysis method (HAM) has been executed for the result of the velocity and temperature. The thickness of the coating film has been kept variable. The pressure distribution under the variable thickness of the liquid film has been calculated. The impacts of different variables and rate of spray during coating have been graphically plotted. The coefficient of skin friction and Nusselt number have been presented numerically. In addition, it is noticed that the thermal field of a nanoliquid elevates with rising values of ϕ and this increase is more in SWCNTs nanofluid than MWCNTs nanofluid.
The population dynamics of two species that is governed by the deterministic Lotka-Volterra model concerned with the interaction of predator and prey is investigated in this article as an application ...of homotopy analysis method. The analytical approximate solution in the form of convergent infinite series is obtained by considering the time-fractional derivatives in the Caputo sense. The simulation of obtained results exhibit the effect of variation in fractional parameters, auxiliary parameters and auxiliary linear operators on the mass concentration of both the biological species which in turn affects the structure of the system.
Lead toxicity became a major concern worldwide and it is one of the most harmful pollutants in soil and groundwater. Hence, to remove lead from the soil, a high efficient technology with improved ...materials and system is required. This paper is a study shows removing of lead ions from soil samples, which have been taken from different sites in the Kurdistan Region, and investigated the adsorption of lead ions on high efficient adsorbent Fe3O4 nanoparticles. The magnetite nanoparticles of 27nm were synthesized by using a co-precipitation method and characterized by X-ray diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR) and scanning electron microscopy (SEM) equipped with energy dispersive X-ray spectroscopy (EDX). The adsorption experiments occurred at pH 8.0 under room temperature (25 °C) and the adsorption capacity was 22.8 mg/g which is 4 times higher than that of coarse particles. The correlation is measured between pH and absorbance, pH and concentration, electrical conductivity and concentration of lead ions in agricultural soil. These relationships indicate that the correlation coefficient values of (r = - 0.68, – 0.70 and + 0.83) are statistically significant at (ɑ= 0.05). The limit of detection (LOD) and limit of quantification (LOQ) were found to be 0.73 mg/L and 2.44 mg/L, respectively.
In current study natural convection flow of second grade fluid in an oscillating infinite vertical cylinder is investigated. The dimensionless governing equations for temperature and velocity are ...obtained by introducing the non-dimensional variables. Exact solutions for temperature and velocity field are computed by means of integral transformation. Solutions for cosine and sine oscillations of velocity field are introduced in the form of transient and post-transient arrangements. A special case for Newtonian fluid is obtained from general results and transients solutions are computed in terms of tables. In the end, the impact of dimensionless numbers (Grashof and Prandtl numbers) at different values of time is presented in graphical form and found that velocity for Newtonian fluid has greater values than the second grade fluid. Furthermore, there are some comparisons of calculated solutions with existing solutions in literature.
The main objective of the study was to understand the notion of Λ-convergence and to study the notion of probabilistic normed (PN) spaces. The study has also aimed to define the statistical ...Λ-convergence and statistical Λ-Cauchy in PN-spaces. The concepts of these approaches have been defined by some examples, which have demonstrated the concepts of statistical Λ-convergence and statistical Λ-Cauchy in PN-spaces. Previous studies have also been used to understand similar terminologies and notations for the extraction of outcomes.
In many industrial applications, heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention, owing to their immense importance in technology, engineering, and ...science. These processes are relevant for polymer solutions, porous industrial materials, ceramic processing, oil recovery, and fluid beds. The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics. Therefore, the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation (quadratic/nonlinear Boussinesq approximation) is performed in the present study. The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow, heat transfer, and entropy generation are analyzed. The governing nonlinear equations are solved with the spectral quasi-linearization method (SQLM). The obtained results are compared with those calculated with a finite element method and the bvp4c routine. In addition, the effects of key parameters on the velocity of the hyperbolic tangent material, the entropy generation, the temperature, and the Nusselt number are discussed. The entropy generation increases with the buoyancy force, the pressure gradient factor, the non-linear convection, and the Eckert number. The non-Newtonian fluid factor improves the magnitude of the velocity field. The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field. The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.
Using the method of Petryshyn's fixed point theorem in Banach algebra, we investigate the existence of solutions for functional integral equations, which involves as specific cases many functional ...integral equations that appear in different branches of non-linear analysis and their applications. Finally, we recall some particular cases and examples to validate the applicability of our study.
In this paper we construct some positive linear operators by means of q-Lagrange polynomials and prove some approximation results via A-statistical convergence. We also define and study the rate of ...A-statistical approximation of these operators by using the notion of modulus of continuity and Lipschitz class.
•Advection reaction susceptible infected recovered (SIR) epidemic model with relapse and immunity loss is considered for numerical analysis in which state variables represent the population ...sizes.•Positivity preserving numerical technique is designed for the epidemic model as state variables are taken in absolute.•The proposed scheme preserves all the important properties possessed by continuous SIR epidemic model.•M-matrix theory is used to prove the positivity of the proposed technique.•Numerical simulations are presented to verify all the attributes of the proposed numerical schemes.
Background and objective: Epidemic models are used to describe the dynamics of population densities or population sizes under suitable physical conditions. In view that population densities and sizes cannot take on negative values, the positive character of those quantities is an important feature that must be taken into account both analytically and numerically. In particular, susceptible-infected-recovered (SIR) models must also take into account the positivity of the solutions. Unfortunately, many existing schemes to study SIR models do not take into account this relevant feature. As a consequence, the numerical solutions for these systems may exhibit the presence of negative population values. Nowadays, positivity (and, ultimately, boundedness) is an important characteristic sought for in numerical techniques to solve partial differential equations describing epidemic models. Method: In this work, we will develop and analyze a positivity-preserving nonstandard implicit finite-difference scheme to solve an advection-reaction nonlinear epidemic model. More concretely, this discrete model has been proposed to approximate consistently the solutions of a spatio-temporal nonlinear advective dynamical system arising in many infectious disease phenomena. Results: The proposed scheme is capable of guaranteeing the positivity of the approximations. Moreover, we show that the numerical scheme is consistent, stable and convergent. Additionally, our finite-difference method is capable of preserving the endemic and the disease-free equilibrium points. Moreover, we will establish that our methodology is stable in the sense of von Neumann. Conclusion: Comparisons with existing techniques show that the technique proposed in this work is a reliable and efficient structure-preserving numerical model. In summary, the present approach is a structure-preserving and efficient numerical technique which is easy to implement in any scientific language by any scientist with minimal knowledge on scientific programming.
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