Asymptotically linear solutions for some linear fractional differential equations

Abstract

We establish here that under some simple restrictions on the functional coefficient a(t) the fractional differential equation 0D(t)(alpha)[tx' - x + x(0)] + a(t)x = 0, t > 0, has a solution expressible as ct + d + o(1) for t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of order alpha is an element of (0, 1) and c, d is an element of R