In this paper, the time-fractional Fisher’s equation (TFFE) is considered to exam the analytical solution using the Laplace q-Homotopy analysis method (Lq-HAM)”. The Lq-HAM is a combined form of q-homotopy analysis method (q-HAM) and Laplace transform. The aim of utilizing the Laplace transform is to outdo the shortage that is mainly caused by unfulfilled conditions in the other analytical methods. The results show that the analytical solution converges very rapidly to the exact solution.

A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon is mostly rising in electromagnetic influences and production of electric signals.  The proposed technique called as He-Fractional Laplace technique with help of Homotopy perturbation is utilized to found the exact and nearly approximated results of differential model and numerical example of telegraph equation or damped wave equation in this article. The most unique term of this technique is that, there is no worry to find the next iteration by integration in recurrence relation. As fractional Laplace integral transformation has some limitations in non-linear terms, to get the result of nonlinear term in

In this paper we find the exact solution of Burger's equation after reducing it to Bernoulli equation. We compare this solution with that given by Kaya where he used Adomian decomposition method, the solution given by chakrone where he used the Variation iteration method (VIM)and the solution given by Eq(5)in the paper of M. Javidi. We notice that our solution is better than their solutions.

The purpose of this paper is to find the best multiplier approximation of unbounded functions in    –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.

      In this paper, a modified three-step iteration algorithm for approximating a joint fixed point of non-expansive and contraction mapping is studied. Under appropriate conditions, several strong convergence theorems and Δ-convergence theorems are established in a complete CAT (0) space. a numerical example is introduced to show that this modified iteration algorithm is faster than other iteration algorithms. Finally, we prove that the modified iteration algorithm is stable. Therefore these results are extended and improved to a novel results that are stated by other researchers. Our results are also complement to many well-known theorems in the literature. This type of research can be played a vital role in computer programming

In the present work, a Z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of the Ag nanoparticles. In this technique, a pulsed second harmonic Nd :YAG laser at wavelength 532 nm was used. The results show that the nonlinear refractive index and nonlinear absorption coefficients of the Ag nanoparticles are found to be dependent on the size these nanoparticles.

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

The research aims to explore the difficulties that encounter teaching geography of cities as perceived by female students. A total of (113) third stage female students / Geography Dept / college of education for women were chosen as a sample for the study. To collect the required data, a questionnaire was used as an instrument; it consisted of six parts represent teaching difficulties. It was a three-point Likert scale instrument with 1 signifying ‘main difficulty, 2 ‘sub-difficulty, and 3 ‘no difficult'. The difficulties organized in descend order, to analyze data, SPSS tool was used. The results revealed that the difficulties of content ranged (2.15-1.18), difficulties of education techniques ranged (2.47-2.04), difficulties of t

 The vast majority of EC applications are the web-based deployed in 3-tire Server-Client environment, the data within such application often resides within several heterogeneous data sources. Building a single application that can access each data sources can be a matter of challenging; this paper concerns with developing a software program that runs transparently against heterogeneous environment for an EC-application.
 

In this paper, we define two operators of summation and summation-integral of q-type in two dimensional spaces. Firstly, we study the convergence of these operators and then we prove Voronovskaya- type asymptotic formulas for these operators.