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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 \(c,d\in\mathbb R\).

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
Full Text: DOI
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