In this paper, the finite difference method is used to solve fractional hyperbolic partial differential equations, by modifying the associated explicit and implicit difference methods used to solve fractional  partial differential equation. A comparison with the exact solution is presented and the results are given in tabulated form in order to give a good comparison with the exact solution

Linear Feedback Shift Register (LFSR) systems are used  widely in stream cipher systems field. Any system of LFSR's which wauldn't be attacked must first construct the system of linear equations of the LFSR unit. In this paper methods are developed to construct a system of linear/nonlinear equations of key generator (a LFSR's system) where the effect of combining (Boolean) function of LFSR is obvious. Before solving the system of linear/nonlinear equations by using one of the known classical methods, we have to test the uniqueness of the solution. Finding the solution to these systems mean finding the initial values of the LFSR's of the generator. Two known generators are used to test and apply the ideas of the paper,

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

      In this paper, several types of space-time fractional partial differential equations has been solved by using most of special double linear integral transform ”double  Sumudu ”. Also, we are going to argue the truth of these solutions by another analytically method “invariant subspace method”. All results are illustrative numerically and graphically.

The Manganese doped zinc sulfide nanoparticles of the cubic zinc blende structure with the average crystallite size of about 3.56 nm were synthesized using a coprecipitation method using Thioglycolic Acid as an external capping agent for surface modification. The ZnS:Mn2+ nanoparticles of diameter 3.56 nm were manufactured through using inexpensive precursors in an efficient and eco-friendly way. X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectroscopy are used to examine the structure, morphology and chemical composition of the nanoparticles. The antimicrobial activity of (ZnS:Mn2+) nanocrystals was investigated by measuring the diameter of inhibition zone using well diffusion mechanism

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.