Positive Solution for Boundary Value Problem of Fractional Di erential Equation

Document Type: Research Articles

Author

Department of Mathematics and Information, Hanshan Normal University, Chaozhou, Guangdong, 521041, P.R. China

Abstract

In this paper, we prove the existence of the solution for boundary value prob-
lem(BVP) of fractional di erential equations of order q 2 (2; 3]. The Kras-
noselskii's xed point theorem is applied to establish the results. In addition,
we give an detailed example to demonstrate the main result.

[1] N. Kosmatov, A singular boundary value problem for nonlinear di erential
equations of fractional order, J. Appl. Math. Comput. 29(2009), 125-135.
[2] S. Zhang, Positive solutions for boundary value problem of nonlinear
fractional di erential equations, Electric. J. Di . Equs. 36 (2006),1-12.
[3] A. P. Chen, Y. S. Tian, Existence of Three Positive Solutions to
Three-Point Boundary Value Problem of Nonlinear Fractional Di erential
Equation, Di er. Equ. Dyn. Syst. 18 (2010), 327-339.
[4] A.A. Kilbsa, H. M. Srivastava, J.J. Trujillo. Theory and Applications of
Fractional Di erential Equations, Elsevier, Amsterdam, 2006.
[5] S. Q. Zhang, Existence results of positive solutions to boundary value
problem for fractional di erential equation, ,Positivity 13(2009), 583-599.
[6] S. Zhang, The existence of a positive solution for a nonlinear fractional
di erential equation, J. Math. Anal. Appl. 252 (2000), 804-812.
[7] S. Zhang, Positive solution for some class of nonlinear fractional
di erential equation, J. Math. Anal. Appl. 278 (2003), 136-148.
[8] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results
for fractional order functional di erential equations with in nite delay, J.
Math. Anal. Appl. 338 (2008), 1340-1350.
[9] D.J. Guo, L. Lakshmikantham, Nonlinear Problems in Abstract Cones,
Academic Press, New York, 1988.