The knowledge of fractional calculus can be useful in developing models that allow us to better understand and manage some phenomena. In the present paper, we study the topological structure of the mild solution set for a semi-linear differential inclusion containing the τ-Caputo fractional derivative in the presence of non-instantaneous impulses and an infinite delay. We demonstrate that this set is non-empty and an Rδ-set. We use a recent result regarding the existence of solutions for τ-Caputo fractional semi-linear differential inclusions. Unlike many results, we do not suppose that the generating semigroup is compact. An illustrative example is given as an application of our results.

In this study, we focused on a subclass of bounded turning functions that are linked with a four-leaf-type domain. The primary goal of this study is to explore the limits of the first four initial coefficients, the Fekete-Szegö type inequality, the Zalcman inequality, the Kruskal inequality, and the estimation of the second-order Hankel determinant for functions in this class. All of the obtained findings have been sharp.

The present study’s intention is to produce exact estimations of some problems involving logarithmic coefficients for functions belonging to the considered subcollection B T sin of the bounded turning class. Furthermore, for the class B T sin , we look into the accurate bounds of the Zalcman inequality, Fekete-Szegö inequality along with D 2 , 1 G g / 2 and D 2 , 2 G g / 2 . Importantly, all of these bounds are shown to be sharp.

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Background. University education in all countries of the world occupies an important placebecause universities are the stronghold of enlightened thought, the center of enlightenment, and the home of constructive scientific research. Through our survey of the published papers, there was no statistical study examining the reasons for this gap. If the reasons are studied, the compatibility between the outputs of education and the labor market will be achieved. Objective. To identify factors that cause the gap between university education and the labor market, then expand the compatibility between learning outcomes in Saudi universities and market requirements in accordance with the Kingdom’s Vision 2030. Methods and Materials. Questionnaires were given to the general population of Saudi Arabia, using Google forms for data collection. The target group was 384 people answered. Results. The findings showed, Resolution IV with regression analysis gave the factors that caused the gap between university education outcomes and the labor market: no training institutions and graduate centers, lack of awareness of children about the appropriate specialties and strengthening their inclinations towards itand the continuous increase in the number of graduates in light of the weak absorptive capacity of the labor market. In addition, the saturated design with regression analysis gave the factors that caused the gap between university education outcomes and the labor market: lack of awareness of children about the appropriate specialties, and strengthening their inclinations towards it and existence of non-national competencies, universities’ lack of materials, and support for the academic content required by the labor market and the continuous increase in the number of graduates in light of the weak absorptive capacity of the labor market, no training institutes and centers for graduates and the continuous increase in the number of graduates in light of the weak absorptive capacity of the labor market. Conclusion. No training institutions and graduate centers, lack of awareness of children about the appropriate specialties and strengthening their inclinations towards it and the continuous increase in the number of graduates in light of the weak absorptive capacity of the labor market are caused the gap between university education outcomes and the labor market.