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In this paper, we research the existence of solutions for a class of Riemann-Liouville fractional evolution inclusions with nonconvex right hand side. Our main results obtain the existence of the extreme solution and the relationship of the solution sets between the original problem and the convexified problem. In the end, we give an example to illustrate the applications of the abstract results.

On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions