Stationary solutions of the fractional kinetic equation with a symmetric power-law potential

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 alpha, 1 less than or equal to alpha less than or equal to 2, are studied analytically and numerically. We show that for 1 less than or equal to alpha < 2, the stationary distribution functions have power-law asymptotic approximations decreasing as x(-)((alpha+2m+1)) for large values of the argument. We also show that these distributions are bimodal.