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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 $c,d\in\Bbb R$.

34A08Fractional differential equations
34D05Asymptotic stability of ODE
34A30Linear ODE and systems, general
Full Text: DOI
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