In this paper, a fractional dynamics approach is used to characterize the observed accelerating expansion of the universe. We claim that the evolution of accelerating expansion obeys an α-exponential function, which is the fundamental solution of linear fractional order dynamical equation. We find that the Hubble constant is 67.8807, 68.2546, and 67.9119 for all redshift z < 1.5, z < 1, and z < 0.1 based on the dataset collected by the Supernova Cosmology Project. Furthermore, we verify that the expansion rate of our universe is speeding up and actually obeys a Mittag-Leffler law.
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Is Our Universe Accelerating Dynamics Fractional Order?
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Zeng, Caibin, Chen, YangQuan, and Podlubny, Igor. "Is Our Universe Accelerating Dynamics Fractional Order?." Proceedings of the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 9: 2015 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications. Boston, Massachusetts, USA. August 2–5, 2015. V009T07A020. ASME. https://doi.org/10.1115/DETC2015-46216
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