A standard theoretical neutron energy flux distribution is achieved for the triton-triton nuclear fusion reaction in the range of triton energy about ≤10 MeV. This distribution give raises an evidence to provide the global calculations including the characteristics fusion parameters governing the T-T fusion reaction.

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

In this paper we have studied a generalization of  a class of ( w-valent ) functions with two fixed points involving hypergeometric function with generalization  integral operator . We obtain some results like, coefficient estimates and some theorems of this class.

Islamic jurisprudence is a divine approach capable of confronting all developments that occur in human society and giving appropriate solutions to them. The research discussed opinions related to some contemporary issues according to the rule of no excess or negligence and according to the rules of removing hardship and facilitating in order to reach the appropriate legal ruling for the nature of the situation to which it may be exposed. Man is in paradise, and the research emphasizes the necessity of taking into account the aspect of precaution when deciding on issues, such as the rules of change and the removal of embarrassment

زاد الاهتمام بالأطفال ذوي اضطراب الانتباه المصحوب بالنشاط الزائد نظراً لانتشاره بين الأطفال في عمر المرحلة الابتدائية حيث تراوحت نسبته ما بين  3% إلى 20%  ومعظمهم من الذكور ، وأن انتشاره يقع في مختلف الطبقات الاجتماعية بالنسبة لعوائل هؤلاء الأطفال كما أن المشكلات المتعلقة به لا تنتهي بانتهاء مرحلة الطفولة ، وغالباً ما تمتد إلى مرحلة المراهقة حيث توصل ويز و هتكمانWeiss&Hechtman,1989  إلى أن هناك علامات م

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu

          We obtain the coefficient estimates, extreme points, distortion and growth boundaries, radii of starlikeness, convexity, and close-to-convexity, according to the main purpose of this paper.