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Mathematics 2016, 4(1), 13; doi:10.3390/math4010013

Existence Results for a New Class of Boundary Value Problems of Nonlinear Fractional Differential Equations

1
Department of mathematics, Central Tehran Branch Islamic Azad university, Tehran 13185/768, Iran
2
Department of Mathematics, Neka Branch Islamic Azad University, Neka 48411-86114, Iran
3
Department of mathematics, Central Tehran Branch Islamic Azad univesity, Tehran 13185/768, Iran
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 27 December 2015 / Revised: 24 February 2016 / Accepted: 25 February 2016 / Published: 4 March 2016
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Abstract

In this article, we study the following fractional boundary value problem D 0 + α c u ( t ) + 2 r D 0 + α 1 c u ( t ) + r 2 D 0 + α 2 c u ( t ) = f ( t , u ( t ) ) , r > 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) , u ( 0 ) = u ( 1 ) , u ( ξ ) + r u ( ξ ) = η , ξ ( 0 , 1 ) Where 2 α < 3 , D 0 + α i c ( i = 0 , 1 , 2 ) are the standard Caputo derivative and η is a positive real number. Some new existence results are obtained by means of the contraction mapping principle and Schauder fixed point theorem. Some illustrative examples are also presented. View Full-Text
Keywords: Fractional boundary value problem; Contraction mapping principle; Schauder fixed point theorem Fractional boundary value problem; Contraction mapping principle; Schauder fixed point theorem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Alvan, M.; Darzi, R.; Mahmoodi, A. Existence Results for a New Class of Boundary Value Problems of Nonlinear Fractional Differential Equations. Mathematics 2016, 4, 13.

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