This paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear time-fractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations.

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This paper investigates some exact and local search methods to solve the traveling salesman problem. The Branch and Bound technique (BABT) is proposed, as an exact method, with two models. In addition, the classical Genetic Algorithm (GA) and Simulated Annealing (SA) are discussed and applied as local search methods. To improve the performance of GA we propose two kinds of improvements for GA; the first is called improved GA (IGA) and the second is Hybrid GA (HGA).

The IGA gives best results than GA and SA, while the HGA is the best local search method for all within a reasonable time for 5 ≤ n ≤ 2000, where n is the number of visited cities. An effective method of reducing the size of the TSP matrix was proposed with

المستخلص:

          في هذا البحث , استعملنا طرائق مختلفة لتقدير معلمة القياس للتوزيع الاسي كمقدر الإمكان الأعظم ومقدر العزوم ومقدر بيز في ستة أنواع مختلفة عندما يكون التوزيع الأولي لمعلمة القياس : توزيع لافي  (Levy) وتوزيع كامبل من النوع الثاني وتوزيع معكوس مربع كاي وتوزيع معكوس كاما وتوزيع غير الملائم (Improper) وتوزيع

Based on nonlinear self- diffraction technique, the nonlinear optical properties of thin slice of matter can be obtained. Here, nonlinear characterization of nano-fluids consist of hybrid Single Wall Carbon Nanotubes and Silver Nanoparticles (SWCNTs/Ag-NPs) dispersed in acetone at volume fraction of 6x10-6, 9x10-6, 18x10-6 have been investigated experimentally. Therefore, CW DPSS laser at 473 nm focused into a quartz cuvette contains the previous nano-fluid was utilized. The number of diffraction ring patterns (N) has been counted using Charge - Coupled- Device (CCD) camera and Pc with a certain software, in order to find the maximum change of refractive index ( of fluids. Our result show that the fraction volume of 18x10-6 is more nonli

The spectral characteristics and the nonlinear optical properties of the mixed donor (C-480) acceptor (Rh-6G) have been determined. The spectral characteristics are studied by recording their absorption and fluorescence spectra. The nonlinear optical properties were measured by z-scan technique, using Q-switched Nd: YAG laser with 1064 nm wavelength. The results showed that the optimum concentration of acceptor is responsible for increasing the absorption and the emission bandwidth of donor to full range and to 242 nm respectively by the energy transfer process, also the efficiency of the process was increased by increasing the donor and acceptor concentration. The obtained nonlinear properties results of the mixture C-480/ Rh-6G showed

This study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim

      The aim of this article is to present the exact analytical solution for models as system of (2+1) dimensional PDEs by using a reliable manner based on combined LA-transform with decomposition technique and the results have shown a high-precision, smooth and speed convergence to the exact solution compared with other classic methods. The suggested approach does not need any discretization of the domain or presents assumptions or neglect for a small parameter in the problem and does not need to convert the nonlinear terms into linear ones. The convergence of series solution has been shown with two illustrated examples such (2+1)D- Burger's system and (2+1)D- Boiti-Leon-Pempinelli (BLP) system.