Asymptotically linear solutions for some linear fractional differential equations (Q624499)

Summary: We establish that under some simple restrictions on the functional coefficient \(a(t)\) the fractional differential equation \[ _0D^\alpha_t[tx'-x+x(0)]+a(t)x=0,\quad t>0, \] has a solution expressible as \(ct+d+o(1)\) for \(t\to+\infty\), where \(_0D^\alpha_t\) designates the Riemann-Liouville derivative of order \(a\in (0,1)\) and \(c,d\in\mathbb R\).