Abstract
The main purpose of this work is to introduce the basic concepts and global properties of the fractional Einstein-Vlasov equation based on the fractional calculus of variations, mainly the fractional actionlike variational approach. We believe that kinetic theory in non-curved spacetimes is fundamental to a good understanding of kinetic theory in general relativity. Besides, the fractional calculus of variations has proved recently to be an important mathematical field of research which has been applied successfully to a broad range of physical and mathematical researches. We expect therefore that the merge of both fields will bring some new insights to general relativity and accordingly to its cosmological and astrophysical implications. Based on the new fractional settings, some cosmological applications are discussed in this work mainly within the aspects of Bianchi spacetimes geometry.
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