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In this article, we deal with the existence of mild solutions for a class of Sobolev type Hilfer fractional equation with non-instantaneous impulses in Banach spaces. By mean of an operator family generated by the operator pairand probability density function, the definition of mild solutions for studied problem was given. The main result is obtained by using the techniques of fractional calculus, measure of noncompactness and Sadovskii fixed point theorem. To the end, an example is given to illustrate the abstract results.

Study on Sobolev type Hilfer evolution equations with non-instantaneous impulses