Opuscula Math. 37, no. 2 (2017), 265-280
http://dx.doi.org/10.7494/OpMath.2017.37.2.265

Opuscula Mathematica

# Fractional boundary value problems on the half line

Assia Frioui
Assia Guezane-Lakoud
Rabah Khaldi

Abstract. In this paper, we focus on the solvability of a fractional boundary value problem at resonance on an unbounded interval. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. The obtained results are illustrated by an example.

Keywords: boundary value problem at resonance, existence of solution, unbounded interval, coincidence degree of Mawhin, fractional differential equation.

Mathematics Subject Classification: 34B40, 34B15.

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• Assia Frioui
• University Guelma, Laboratory of Applied Mathematics and Modeling, P.O. Box 401, Guelma 24000, Algeria
• Assia Guezane-Lakoud
• University Badji Mokhtar-Annaba, Faculty of Sciences, Laboratory of Advanced Materials, P.O. Box 12, 23000, Annaba, Algeria
• Rabah Khaldi
• University Badji Mokhtar-Annaba, Faculty of Sciences, Laboratory of Advanced Materials, P.O. Box 12, 23000, Annaba, Algeria
• Communicated by Jean Mawhin.
• Revised: 2016-05-13.
• Accepted: 2016-06-02.
• Published online: 2017-01-03.