Boundary value problems for nonlinear fractional differential equations

Benbachir Maamar

DOI Number
-
First page
157
Last page
168

Abstract


Sufficient conditions are given in this paper for the existence of solutions of the boundary value problems for nonlinear fractional differential equationsinvolving Riemman fractional derivatives operator of arbirary order. The results are obtained using Banach contraction principle and Krasnoselskii's fixed point theorem.

Keywords


Riemann-Liouville derivative; Boundary Value Problem; ; fixed point theorem, local conditions

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References


S. Abbas, M. Benchohra, G.M. N'Guérékata, Topics in Fractional Differential Equations, Springer, NewYork, 2012.

A. Saadi, M. Benbachir, Positive solutions for three-point nonlinear fractional boundary value problems, E. J. Qualitative Theory of Diff. Equ, 3 (2011) 1-19.

A. Saadi, A. Benmezai, M. Benbachir,Positive Solutions to Three-point Nonlinear Fractional Semi-positone Boundary Value Problem, PanAmerican Mathematical Journal, Volume 22(2012), Number 4, 41--57.

M. A. Krasnosel'skii, Topological Methods in the Theory on Nonlinear Integral Equations, (English) Translated by A. H. Armstrong; A Pergamon Press Book, MacMillan, New York, 1964.

V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.


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ISSN 0352-9665 (Print)
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