Geodesic
Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 2, pp. 169-189.

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The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
Keywords: fractional differential equation, half-line, Krasnoselsk'ii's fixed point theorem, existence, positive solution 
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Boucenna, Amina; Moussaoui, Toufik. Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 2, pp. 169-189. http://geodesic.mathdoc.fr/item/DMDICO_2014_34_2_a1/

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