Geodesic
A~boundary-value problem for a~non-linear equation with a~fractional derivative
Izvestiya. Mathematics , Tome 73 (2009) no. 6, pp. 1173-1196

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We consider a problem on a half-line with a Neumann-type boundary condition. We prove the global existence of solutions and find the leading term of their large-time asymptotic expansion. The case of large initial data and critical non-linearity is considered in the case when the non-linear term of the equation decays in time as rapidly as the linear terms.
Keywords: Neumann-type boundary-value problem, non-linear equation, fractional derivative, asymptotic behaviour. 
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     title = {A~boundary-value problem for a~non-linear equation with a~fractional derivative},
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E. I. Kaikina; P. I. Naumkin; I. A. Shishmarev. A~boundary-value problem for a~non-linear equation with a~fractional derivative. Izvestiya. Mathematics , Tome 73 (2009) no. 6, pp. 1173-1196. http://geodesic.mathdoc.fr/item/IM2_2009_73_6_a4/