International Journal of Differential Equations

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

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

Erratum

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

A. Guezane-Lakoud and R. Khaldi

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 , .

Equation must be

The Green function in is

Equation becomes

Equation must be

Equation must be

In Theorem 3.2, the condition must be

Equation must be

and becomes

Equation is

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation becomes

Equation is as follows:

Equation is as follows:

Equation becomes

Equation is

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

(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 is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

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

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Equation is as follows:

Let

Equation is as follows:

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

Equation is as follows:

Equation is as follows:

Equation is as follows:

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 .