Imed Bachar, Habib Maagli
Abstract:
In this article, we study the superlinear fractional
boundary-value problem
where
,
is the Riemann-Liouville
fractional derivative and
are such that
.
The function
that may be singular at x=0 and x=1 is required to satisfy
convenient hypotheses to be stated later.
By means of a perturbation argument, we establish the existence,
uniqueness and global asymptotic behavior of a positive continuous solution
to the above problem.An example is given to illustrate our main results.
Submitted February 8, 2016. Published April 26, 2016.
Math Subject Classifications: 34A08, 34B15, 34B18, 34B27.
Key Words: Fractional differential equation; positive solution;
Green's function; perturbation arguments.
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Imed Bachar King Saud University, College of Science Mathematics Department, P.O. Box 2455 Riyadh 11451, Saudi Arabia email: abachar@ksu.edu.sa | |
Habib Mâagli King Abdulaziz University, Rabigh Campus College of Sciences and Arts, Department of Mathematics P.O. Box 344, Rabigh 21911, Saudi Arabia email: abobaker@kau.edu.sa, habib.maagli@fst.rnu.tn |
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