On the Fractional Pettis and Aumann-Pettis Integral for Multifunctions

Let $\alpha$ be a positive real number. In the present paper we present the definition of the Aumann Pettis integral and the Pettis integral of order $\alpha$ for multifunctions. The properties of these integrals and the relations between them are studied extensively. In particular, a Strassen type theorem in this case and continuation property are proved. Also, we give a version for Fatou's lemma and dominated convergence theorem for the Aumann-Pettis integral of order $\alpha$ and for multifunctions.