Abstract
The properties of stationary solutions of the one-dimensional fractional Einstein--Smoluchowski equation with a potential of the form x 2m+2, m = 1, 2,..., and of the Riesz spatial fractional derivative of order α, 1 ≤ α ≤ 2, are studied analytically and numerically. We show that for 1 ≤ α < 2, the stationary distribution functions have power-law asymptotic approximations decreasing as x −(α+2m+1) for large values of the argument. We also show that these distributions are bimodal.
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Gonchar, V.Y., Tanatarov, L.V. & Chechkin, A.V. Stationary Solutions of the Fractional Kinetic Equation with a Symmetric Power-Law Potential. Theoretical and Mathematical Physics 131, 582–594 (2002). https://doi.org/10.1023/A:1015118206234
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DOI: https://doi.org/10.1023/A:1015118206234