This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

هدف البحث إلى إعداد تمرينات منطقة الشدة الثالثة للقوة المميزة بالسرعة للرجلين للاعبين الشباب بكرة القدم، والتعرف على تأثير تمرينات منطقة الشدة الثالثة للقوة المميزة بالسرعة للرجلين في السرعة الانتقالية وفي سرعة التهديف للاعبين الشباب بكرة القدم، وأفترض الباحث بأنه توجد فروق ذات دلالة إحصائية بين نتائج الاختبارات القبلية والبعدية لمجموعتي البحث التجريبية والضابطة لكل من السرعة الانتقالية وسرعة التهديف ب

The research aimed to prepare a measure of the importance of enlightenment, academic education, and applied skills for third-stage female students, including teaching methods from their point of view/College of Education and Sports Sciences/University of Baghdad/Al-Jadriyah. The researchers used descriptive description in the comprehensive research procedures, an appropriate methodology in achieving the research objectives, sufficient for interpretations, how important is the academic teacher’s knowledge of teaching methods for student learning, what are the roles that the learners have acquired from the academic teacher. The scale of importance and horror consists of 15 items. The research population includes female students of t

The research aimed to prepare a measure of the importance of enlightenment, academic education, and applied skills for third-stage female students, including teaching methods from their point of view/College of Education and Sports Sciences/University of Baghdad/Al-Jadriyah. The researchers used descriptive description in the comprehensive research procedures, an appropriate methodology in achieving the research objectives, sufficient for interpretations, how important is the academic teacher’s knowledge of teaching methods for student learning, what are the roles that the learners have acquired from the academic teacher. The scale of importance and horror consists of 15 items. The research population includes female students of t

In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that suppo