International Journal of Differential Equations

Volume 2013 (2013), Article ID 852851, 5 pages

http://dx.doi.org/10.1155/2013/852851

## Erratum to “Positive Solution to a Fractional Boundary Value Problem”

Laboratory of Advanced Materials, Faculty of Sciences, University Badji Mokhtar-Annaba, P.O. Box 12, 23000 Annaba, Algeria

Received 17 February 2013; Accepted 14 April 2013

Copyright © 2013 A. Guezane-Lakoud and R. Khaldi. 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.

In the paper entitled “Positive solution to a fractional boundray value problems,” the following problem (P1) is studied: where is a given function, , and . Remarking that all the calculuses in this paper are done for and that if we take , then and the second derivative with respect to of is discontinuous for , consequently we cannot apply this method to establish the existence and positivity of solution. For this reason, we correct the study of problem (P1) by taking , and then the following corrections are needed.

In page 3, in Lemma 2.3, we should correct , .

In Theorem 3.2, the condition must be

(H2) .

In Lemma 4.1, we have and becomes:

If , , then

Equation should be which is positive if .

Equation : let ; it is easy to see that , and then we have Finally, since is nonnegative, we obtain .

In Lemma 4.3, put and inequality becomes

Equation : in view of the left hand side of , we obtain for all

Let

Using the left hand side of and Lemma 4.1, we obtain :

In Example 4.6, if we choose ; then we get the same results with

In Example 4.7, choose , , and ; then we get the same results.

*Remark 1. *
One can study the problem (P1) for and the function depending only on and instead of .