# Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Amina Boucenna; Toufik Moussaoui

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2014)

- Volume: 34, Issue: 2, page 169-189
- ISSN: 1509-9407

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topAmina Boucenna, and Toufik Moussaoui. "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 34.2 (2014): 169-189. <http://eudml.org/doc/270584>.

@article{AminaBoucenna2014,

abstract = {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.},

author = {Amina Boucenna, Toufik Moussaoui},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {fractional differential equation; half-line; Krasnoselsk'ii's fixed point theorem; existence; positive solution; Krasnosel'skii's fixed point theorem},

language = {eng},

number = {2},

pages = {169-189},

title = {Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line},

url = {http://eudml.org/doc/270584},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Amina Boucenna

AU - Toufik Moussaoui

TI - Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2014

VL - 34

IS - 2

SP - 169

EP - 189

AB - 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.

LA - eng

KW - fractional differential equation; half-line; Krasnoselsk'ii's fixed point theorem; existence; positive solution; Krasnosel'skii's fixed point theorem

UR - http://eudml.org/doc/270584

ER -

## References

top- [1] C. Corduneanu, Integral Equations and Stability of Freedback Systems (Academic Press, New York, 1973).
- [2] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones (Academic Press, New York, 1988). Zbl0661.47045
- [3] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Amsterdam, 2006). Zbl1092.45003
- [4] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego 1999).
- [5] X. Su and S. Zhang, Unbounded solutions to a boundary value problem of fractional order on the half-line, Comp. Math. Appl. 61 (2011) 1079-1087. doi: 10.1016/j.camwa.2010.12.058 Zbl1217.34045
- [6] E. Zeidler, Nonlinear Functional Analysis, T1, Fixed Point Theory (Springer 1985).

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