In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

      The method of coordinate conversion is still considered important and laborious due to the shift from the spatial ellipsoidal (geographic) to the flat planned system. The most common method uses a contiguous UTM system as one of the most reliable systems in the conversion process; however, this system faces a problem in large areas that contain more than one zone. The goal of this research is to create a simple and low computational cost model to represent a non-contiguous semi-UTM geographic coordinates for confined regions of the globe. The considered region taken in this study is the northern parts of Arabian Gulf (including parts of Iraq, Kuwait, Iran, and Saudi Arabia). The determined mathematical mode

In this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex. 

     In this paper, a general expression formula for the Boubaker scaling (BS) operational matrix of the derivative is constructed. Then it is used to study a new parameterization direct technique for treating calculus of the variation problems approximately. The calculus of variation problems describe several important phenomena in mathematical science. The first step in our suggested method is to express the unknown variables in terms of Boubaker scaling basis functions with unknown coefficients. Secondly, the operational matrix of the derivative together with some important properties of the BS are utilized to achieve a non-linear programming problem in terms of the unknown coefficients. Finally, the unknown parameters are obtaine

The main goal of this paper is to study and discuss a new class of meromorphici "functions[ which are multivalent defined by [fractional  calculus operators. Coefficients iestimates , radiisi of satarlikeness , convexityi and closed-to-iconvexity are studied. Also distortion iand closure theorems for the classi" ,  are considered.

In this paper we introduced a new type of integrals based on binary element sets “a generalized integral of Shilkret and Choquet integrals” that combined the two kinds of aggregation functions which are Shilkret and Choquet integrals. Then, we gave some properties of that integral. Finally, we illustrated our integral in a numerical example.
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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

The study aims at figuring out the intended meaning of intonation in some English conversational utterances together with identifying pitch variations that are determined by various syntactic constructions that impart the same illocutionary force of utterances. However, intonation is needed to delimit the communicative forces of utterances by virtue of its structure which the speakers intend to convey .This paper consists of four sections .Section one deals with phonology and its types .Section two discusses intonation in relation to style , forms and functions. Section three sheds some light on pragmatics. Section four deals in details with the intended meaning of intonation in some English conversational utterances. This paper comes up wi

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica^®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between t