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Asymptotically linear solutions for some linear fractional differential equations. (English) Zbl 1210.34005
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 \(c,d\in\mathbb R\).

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
34D05 Asymptotic properties of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems, general
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