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We study representations of positive definite kernels K in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for the most general given positive definite kernel, but are then subsequently specialized to the above mentioned applications. Given a positive definite kernel K on...
Blood flow through the composite stenosis of a micro vessel with permeable walls in the presence of an external magnetic field was examined. Endothelial walls of blood vessels are considered to be highly permeable in nature. Thus in the study of such flows, wall permeability must be accounted for. Blood flow made up of a particle-fluid suspension in the core surrounded by a plasma layer was utilized...
In this paper, we employ collocation method using a new orthogonal polynomial (Chelyshkov polynomials) to find the numerical solution of two-dimensional Fredholm–Volterra integral equations. Here, we consider two-dimensional Chelyshkov polynomials and their operational matrix. This method transforms the integral equation to a system of linear algebraic equations by means of collocation points. This...
Flow of a Eyring–Powell fluid in a scraped surface heat exchangers (SSHEs) is analyzed. Foodstuff behaves as non-Newtonian material so for studying non-Newtonian effects inside SSHE Eyring–Powell fluid model is considered. As every physical phenomena can be interpreted mathematically therefore in this work we mathematically studied flow inside SSHE. Steady isothermal incompressible flow of Eyring–Powell...
In this current paper, we present a numerical method to solve a class of fractional optimal control problems of system described by integer-fractional derivative. The fractional derivative is explained in the Caputo sense and a new formulation for the Bernoulli Caputo fractional derivative operational matrix has been achieved for the first time. Then this matrix and operational matrix of multiplication...
The effect of time dependent body forces on the propagation of SH-type wave motion in visco-elastic half space is considered in this paper. The surface displacement component is obtained in a closed form. Numerical results are obtained for a particular case of time dependent body force at different distances from the source for the different values of the non-dimensional time. The results are shown...
In this paper, the parametric optimization method is used to solve a class of fractional optimal control problems. The solution is based on state parametrization, as a linear combination of shifted Legendre polynomials with unknown coefficients. An iterative algorithm is proposed for computing optimal coefficients. In this method the state and control variables can be approximated as a function of...
Drug abuse is an issue of considerable concern due to its association with numerous public health problems. Mathematical models developed to describe the spread of drug abuse have generally assumed that the dynamics of drug use and treatment are substantially the same for women as men. However, research has revealed that the dynamics of women’s drug use and treatment are different in many ways from...
In this paper, He’s frequency-amplitude formulation with some choice of location points that improve accuracy is applied to determine the periodic solution for the nonlinear oscillations of a point charge in the electric field of charged ring. The frequency of the oscillator system can be obtained using concise and straight-forward calculation steps. Good agreement between the results from the proposed...
The solution of fully coupled system of equations governing the axisymmetric quasi-static deformation of a poroelastic medium with anisotropic permeability is employed to obtain the expressions for pore pressure, stresses and displacements in a soil stratum overlying a smooth-rigid pervious or impervious base. Both fluid as well as solid constituents are taken to be compressible. We use the stiffness...
In this article, the single term Walsh series (STWS) method is presented to solve the system of nonlinear delay Volterra integro-differential equations, which arises in biology. The STWS method reduces the model problem into recursive system of nonlinear algebraic equations. The solutions of the algebraic equations lead to the solution of the problem. Illustrative examples related to the biological...
In this paper, power series solutions for strong spherical shocks of time dependent variable energy propagating in a two-phase gas–particle medium are presented taking into consideration the power series solution technique (Sakurai in J Phys Soc Jpn 8:662–669, 1953; Freeman in J Phys D Appl Phys 2(1):1697–1710, 1968). Assuming the medium to be a mixture of a perfect gas and small solid particles,...
The effects of Soret and Dufour on thermophoertic MHD radiative flow and heat transfer over a non-linear stretching sheet have been investigated. Chemical reaction is also taken into consideration. Suitable similarity transformations are used to solve the governing partial differential equation. The resulting non-dimensional governing equations are solved numerically by the fourth fifth order Runge–Kutta...
In this paper we consider a class of degenerate viscoelastic wave equation with density in Kirchhoff-type. Under appropriate conditions on the initial datums, we prove a very general decay rate of solution using the Lyapunov functions. In order to compensate the lack of Poincare’s inequality in $$\mathbb {R}^{n}$$ Rn , we use spaces weighted by density function.
Role of intuitionistic fuzzy sets (IFSs) in solving multiple attribute decision making (MADM) problem has been established by many researchers. Depending upon the situation, we need different types of entropies based on IFSs. In this paper, we have proposed a new two parametric intuitionistic fuzzy entropy in the settings of IFSs theory. Besides proving some major properties, the proposed entropy...
A problem of mixed convective flow of a non-Newtonian power-law fluid over an inclined plate embedded in a non-Darcy porous medium under convective thermal boundary condition is attempted in the present investigation. In addition, the nonlinear temperature–concentration-dependent density relation taken into account to address thermal and solutal transport phenomena in some thermal systems which are...
The purpose of the present paper is to analyze the channel coordination of a manufacturer and a retailer when demand is stochastic and dependent on the promotional effort. The manufacturer produces goods and delivers to the retailer prior the selling session. Then the retailer sells the items during the selling session. Both the members of the supply chain make their expected profits by trading off...
This paper deals with an approximate analytical solution of multi-dimensional, time-fractional coupled viscous Burgers’ equation obtained by employing “homotopy perturbation method” where fractional derivative is of Caputo type. Three test problems are carried out in order to validate and illustrate the efficiency of the method for TFCB equation. The results are also depicted in graphically for different...
The heat function concept has been developed for the heatline visualization to study the conjugate heat transfer effects at large Grashof number. The time-dependent natural convective micropolar fluid flow past a vertical slender hollow cylinder with the inner wall kept at a uniform temperature is the physical model. The mathematical model of this problem is given by highly time reliant non-linear...
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