Transformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s Polynomials is provided as the transformation plays an essential role in solving differential linear and non-linear equations. Here is the α-Sumudu technique to find the relevant results of the gas dynamics equation in fractional order. To calculate the non-linear fractional gas dynamical problem, a consumer method created on the new homotopy perturbation a-Sumudu transformation method (HP TM) is suggested. In the Caputo type, the derivative is evaluated. a-Sumudu homotopy pe

Todays, World is faced an energy crisis because of a continuous increasing the consumption of fuels due to intension demand for all types of vehicles. This study is one of the efforts dealing with reduce the weight of vehicles by using a new material of sandwich steel, which consists of two skin steel sheets with core of a polymer material. Resistance spot welding (RSW) can be easily implemented on metals; however a cupper shunt tool was designed to perform the resistance welding of sandwich steel with DP800 cover sheets to resolve a non-conductivity problem of a polymer core. Numerical simulations with SORPAS^®3D were employed to test the weldability of this new material and supported by many practical experiments. In conclus

Abstract:

One of the important things provided by fuzzy model is to identify the membership functions. In the fuzzy reliability applications with failure functions of the kind who cares that deals with positive variables .There are many types of membership functions studied by many researchers, including triangular membership function, trapezoidal membership function and bell-shaped membership function. In I research we used beta function. Based on this paper study classical method to obtain estimation fuzzy reliability function for both series and parallel systems.

    In this paper, we introduce new conditions to prove that the existence and boundedness of the solution by convergent sequences and convergent series. The theorem of Krasnoselskii, Lebesgue’s dominated convergence theorem and fixed point theorem are used to get some sufficient conditions for the existence of solutions. Furthermore, we get sufficient conditions to guarantee the oscillatory property for all solutions in this class of equations. An illustrative example is included as an application to the main results.

In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.

The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.

 Abstract

Basra province is known for its logistic location for trading activity and oil industry. By geological point of view, Basra areas are believed to consist mainly of alternation of (clay, silty clay, clayey silt, silt and sand) type of soil. Any development of industry in this area should be affected by the occurrence of the clay soil. That is why the investigation to the soil is more than necessary. In this case, a vast testing program was carried out by the author to evaluate the various formations constituting the of some Basra soils. An attempt to characterize and discuss the nature, minerals, engineering behavior and field properties of soil samples extracted from more than one thousand and one