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This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#945;</mi> <mo>&#8712;</mo> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. The main tools of our study include the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed-point theorem. As an application, we apply the obtained results to a control problem.