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This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.

In this paper we will try to reach a twofold goal. First we will give an analysis of mathematical terminology in order to give practical hints for assigning subject headings to a book. Secondly, we will propose a method which could be helpful for the subject analysis of a given document. The main basis for this method is the connection between a special classification scheme, the Subject Classification Scheme of the American Mathematical Society, and the task of indexing books by subject headings. Examples of this method are given, and they are compared with Library of Congress Subject Headings and PRECIS entries. With both the study of the terminology and the proposed method, it should be possible to increase quality and consistency of the library indexing results for mathematical books. A thesaurus for mathematics with entries along the lines of the PRECIS rules and connected with the subject classification scheme of the American Mathematical Society, would be desirable, as would the printing of appropriate classification data, assigned to them by their authors, inside the books.