The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

The proposal of nonlinear models is one of the most important methods in time series analysis, which has a wide potential for predicting various phenomena, including physical, engineering and economic, by studying the characteristics of random disturbances in order to arrive at accurate predictions.

In this, the autoregressive model with exogenous variable was built using a threshold as the first method, using two proposed approaches that were used to determine the best cutting point of [the predictability forward (forecasting) and the predictability in the time series (prediction), through the threshold point indicator]. B-J seasonal models are used as a second method based on the principle of the two proposed approaches in dete

Water level and distribution is very essential in almost all life aspects. Natural and artificial lakes represent a large percentage of these water bodies in Iraq. In this research the changes in water levels are observed by calculating the areas of five different lakes in five different regions and two different marshes in two different regions of the country, in a period of 12 years (2001 - 2012), archived remotely sensed images were used to determine surface areas around lakes and marshes in Iraq for the chosen years . Level of the lakes corresponding to satellite determined surface areas were retrieved from remotely sensed data .These data were collected to give explanations on lake level and surface area fluctuations. It is imp

Abstract: A novel design of Mach Zehnder Interferometer (MZI) in terms of using special type of optical fiber that has double clad with graded distribution of the refractive index that can be easily implemented practically was suggested and simulated in this work. The suggested design is compact, rapid, and is simple to be modified and tested. The simulated design contains a MZI of 1546.74 nm of central wavelength that is constructed using special type of double clad optical fiber that has two different numerical apertures. The first aperture will supply single mode propagation via its core, while the second numerical aperture supports a zigzag wave propagation (multimode) in the first clad region. The interferometer’s

This paper presents on the design of L-Band Multiwavelength laser for Hybrid Time Division Multiplexing/ Wavelength Division Multiplexing (TDM/WDM) Passive Optical Network (PON) application. In this design, an L-band Mulltiwavelength Laser is designed as the downstream signals for TDM/WDM PON. The downstream signals ranging from 1569.865 nm to 1581.973 nm with 100GHz spacing. The multiwavelength laser is designed using OptiSystem software and it is integrated into a TDM/WDM PON that is also designed using OptiSystem simulation software. By adapting multiwavelength fiber laser into a TDM/WDM network, a simple and low-cost downstream signal is proposed. From the simulation design, it is found that the proposed design is suitable to be used

Catalytic reforming of naphtha occupies an important issue in refineries for obtaining high octane gasoline and aromatic compounds, which are the basic materials of petrochemical industries. In this study, a novel of design parameters for industrial continuous catalytic reforming reactors of naphtha is proposed to increase the aromatics and hydrogen productions. Improving a rigorous mathematical model for industrial catalytic reactors of naphtha is studied here based on industrial data applying a new kinetic and deactivation model. The optimal design variables are obtained utilizing the optimization process in order to build the model with high accuracy and such design parameters are then applied to get the best configuration of this pro

The development of the perforated fin had proposed in many studies to enhance the heat transfer from electronic pieces. This paper presents a novel derivative method to find the temperature distribution of the new design (inclined perforated) of the pin fin. Perforated with rectangular section and different angles of inclination was considered. Signum Function is used for modeling the variable heat transfer area. Set of parameters to handle the conduction and convection area were calculated. Degenerate Hypergeometric Equation (DHE) was used for modeling the Complex energy differential equation and then solved by Kummer’s series. In the validation process, Ansys 16.0-Steady State Thermal was used. Two geometric models were consider