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Zbl 1217.34045
Su, Xinwei; Zhang, Shuqin
Unbounded solutions to a boundary value problem of fractional order on the half-line. (English)
[J] Comput. Math. Appl. 61, No. 4, 1079-1087 (2011). ISSN 0898-1221

Summary: This paper deals with a boundary value problem of a fractional differential equation with the nonlinear term dependent on a fractional derivative of lower order on the semi-infinite interval. An appropriate compactness criterion is established, such that we can use Schauder's fixed point theorem on an unbounded domain to obtain the existence result for solutions. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded. An example illustrating our main result is also given.

MSC 2000:: *34B40 Boundary value problems on infinite intervals
26A33 Fractional derivatives and integrals (real functions)
34A08
34C11 Qualitative theory of solutions of ODE: Growth, etc.
45J05 Integro-ordinary differential equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional differential equation; boundary value problem; unbounded solution; infinite interval; fixed point theorem

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