In this paper, we introduce new labeling and named it as k-total edge mean cordial (k-TEMC) labeling. We study certain classes of graphs namely path, double comb, ladder and fan in the context of 3-TEMC labeling.
In this paper, we study the outcome of fractional Laplace transform using inverse difference operator with shift value. By the definition of convolution product, the properties of fractional transformation, the relation between convolution product and fractional frequency Laplace transform with shift value have been discussed. Further, the connection between usual Laplace transform and fractional frequency Laplace transform with shift value are also presented. Numerical examples with graphs are verified and generated by MATLAB.
This paper presents Caputo-Fabrizio fractional derivatives approach to analysis of a viscous fluid over an infinite flat plate together with general boundary motion. Closed form exact general solutions of the fluid velocity are obtained by means of the Laplace transform. The solutions of ordinary viscous fluids corresponding to time-derivatives of integer order is obtained as particular cases of the present solutions. Several special cases are also discussed. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter \(\alpha\) and Reynolds number on velocity field.
The boundary value problems in Kinetic theory of gases, elasticity and other applied areas are mostly reduced in solving single variable nonlinear equations. Hence, the problem of approximating a solution of the nonlinear equations is important. The numerical methods for finding roots of such equations are called iterative methods. There are two type of iterative methods in literature: involving higher derivatives and free from higher derivatives. The methods which do not require higher derivatives have less order of convergence and the methods having high convergence order require higher derivatives. The aim of present report is to develop an iterative method having high order of convergence but not involving higher derivatives. We propose three new methods to solve nonlinear equations and solve text examples to check validity and efficiency of our iterative methods.
In this paper, we obtain the boundedness of commutators generated by the Calderón-Zygmund operator, BMO functions and Lipschitz function on Herz-Morrey-Hardy spaces with variable exponent \(HMK^{\alpha(\cdot),q}_{p(\cdot),\lambda}(\mathbb{R}^{n})\).
In this paper we present a new method to compute the determinants of square matrices of order 5 and 6. To prove the main results we have combined the Farhadian’s Duplex Fraction method and Salihu’s method to reduce the order of determinants to second order. Hence, this paper gives the possibility to develop a general method to compute the determinants of higher order.
Some new inequalities of Simpson’s type for functions whose third derivatives in absolute value at some powers are strongly \((s,m)\)- convex in the second sense are provided. An application to the Simpson’s quadrature rule is also provided.
This paper investigates the squeezing flow of an electrically conducting magnetohydrodynamic Casson nanofluid between two parallel plates embedded in a porous medium using differential transformation and variation of parameter methods. The accuracies of the approximate analytical methods for the small and large values of squeezing and separation numbers are investigated and established. Good agreements are established between the results of the approximate analytical methods are compared with the results numerical method using fourth-fifth order Runge-KuttaFehlberg method. However, the results of variation of parameter methods show better agreement with the results of numerical method than the results of differential transformation method. Thereafter, the developed approximate analytical solutions are used to investigate the effects of pertinent flow parameters on the squeezing phenomena of the nanofluids between the two moving parallel plates. The results established that the squeezing number and magnetic field parameters decrease as the flow velocity increases when the plates were coming together. Also, the velocity of the nanofluids further decreases as the magnetic field parameter increases when the plates move apart. However, the velocity is found to be directly proportional to the nanoparticle concentration during the squeezing flow i.e. when the plates are coming together and an inverse variation between the velocity and nanoparticle concentration is recorded when the plates are moving apart. As increased physical insights into the flow phenomena are provided, it is hope that this study will enhance the understanding the phenomena of squeezing flow in various applications such as power transmission, polymer processing and hydraulic lifts.
In the field of computer networks, the performance of data transmission is usually characterized by the fractional factor. Some sufficient conditions for the existence of Hamilton fractional factors are obtained in this paper, and they extend the original theory presented in Gao et al. [1].
In this paper we are concerned with the problem of asymptotic integration of positive solutions of higher order fractional differential equations with Caputo-type Hadamard derivative of the form \(^{C,H}D_{a}^r x(t)=e(t)+f(t,x(t)), \; a>1,\) where \(r = n +\alpha -1, \alpha\in (0, 1), n \in \mathbb{Z}^+\). We shall apply our technique to investigate the oscillatory and asymptotic behavior of all solutions of the integral equation \(x(t)=e(t)+\int_a ^t (\ln\frac{t}{s} )^{r-1} k(t,s)f(s,x(s))\frac{ds}{s}, \; a>1,\) \(r\) is as above.
