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 .