No Access

Existence of solutions for a higher order fractional boundary value problem posed on the half-line

A. Boucenna

Laboratory of Fixed Point Theory and Applications, Department of Mathematics, E.N.S., Kouba, Algiers, Algeria

E-mail Address: boucenna-amina@hotmail.fr

Search for more papers by this author

and

T. Moussaoui

Laboratory of Fixed Point Theory and Applications, Department of Mathematics, E.N.S., Kouba, Algiers, Algeria

E-mail Address: moussaoui@ens-kouba.dz

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S1793557119500086Cited by:0 (Source: Crossref)

Abstract

The aim of this paper is to study the existence and uniqueness of solutions for a boundary value problem associated with a fractional nonlinear differential equation with higher order posed on the half-line. An appropriate continuous embedding for suitable Banach spaces are proved and the Minty–Browder theorem for monotone operators is used in the proof of existence of solutions for a boundary value problem of fractional order posed on the half-line.

Communicated by H. M. Srivastava

Keywords:

AMSC: 47H05, 26A33

References

1. A. Boucenna, T. Moussaoui and D. O’Regan, Existence of solutions for a boundary value problem of fractional order on the half-line via monotone theory, Int. J. Differ. Appl. 15(1) (2016) 55–68. Google Scholar
2. H. Brezis, Analyse Fonctionnelle, Théorie et Applications (Masson, Paris, 1983). Google Scholar
3. C. Corduneanu, Integral Equation and Stability of Feedback Systems (Academic Press, New York, 1973). Google Scholar
4. A. Friedman, Foundations of Modern Analysis (Dover Publications, Inc, New York, 1982). Google Scholar
5. L. Gasinski and N. S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems (Chapman-Hall CRC, 2005). Google Scholar
6. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier Science, Amsterdam, 2006). Google Scholar
7. J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (Dunod, Paris, 1969). Google Scholar
8. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999). Google Scholar
9. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integral and Derivatives: Theory and Applications (Gordon and Breach Science Publishers, 1993). Google Scholar
10. E. Zeidler, Nonlinear Functional Analysis and Its Applications, II/B, (Springer-Verlag, Berlin, New York, 1986). Crossref, Google Scholar