Electron. J. Differential Equations, Vol. 2017 (2017), No. 240, pp. 1-16.

Positive solutions for superlinear Riemann-Liouville fractional boundary-value problems

Imed Bachar, Habib Maagli, Vicentiu D. Radulescu

Using a perturbation argument, we establish the existence and uniqueness of a positive continuous solution for the following superlinear Riemann-Liouville fractional boundary-value problem
 D^{\alpha }u( x) -u(x)\varphi (x,u(x))=0,\quad 0<x<1,\cr
 u(0)=u'(0)=\lim_{x\to 0^{+}} x^{4-\alpha}u''(x)=0,\quad u''(1)=a>0,
where $3<\alpha \leq 4$ and $\varphi (x,t)$ satisfies a suitable integrability condition.

Submitted August 18, 2017. Published October 4, 2017.
Math Subject Classifications: 34A08, 34B15, 34B18, 34B27.
Key Words: Fractional differential equation; positive solution; Green's function; perturbation; Schauder fixed point theorem.

Show me the PDF file (275 KB), TEX file for this article.

Imed Bachar
King Saud University
Department of Mathematics, College of Science
P.O. Box 2455, Riyadh 11451, Saudi Arabia
email: abachar@ksu.edu.sa
Habib Mâagli
Department of Mathematics
College of Sciences and Arts
King Abdulaziz University
Rabigh Campus P.O. Box 344
Rabigh 21911, Saudi Arabia
email: abobaker@kau.edu.sa, habib.maagli@fst.rnu.tn
Vicentiu D. Radulescu
Department of Mathematics
Faculty of Sciences
King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia
email: vicentiu.radulescu@math.cnrs.fr

Return to the EJDE web page