AbstractIn this paper we study fractional differential inclusions in the sense of Almgren. We begin with a discussion of multiple-valued functions in the Almgren sense and include the basic results needed to make the paper selfcontained. Sufficient background on the fractional calculus is provided to make the material accessible also to the non-specialist readers. Our main result gives sufficient conditions for the existence of at least one solution to the problem under investigation. In

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... n, we show that the solution set to the problem is compact.