Positive solution for boundary value problem of fractional dierential equation

Subject Areas : Applied Mathematics

Haidong Qu ¹

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

Received: 2015-09-28 Accepted : 2015-09-28 Published : 2013-12-01

Keywords:

Abstract :

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential 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.

References:

[1] N. Kosmatov, A singular boundary value problem for nonlinear dierential
equations of fractional order, J. Appl. Math. Comput. 29 (2009), 125-135.
[2] S. Zhang, Positive solutions for boundary value problem of nonlinear
fractional dierential 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 Dierential
Equation, Dier. Equ. Dyn. Syst. 18 (2010), 327-339.
[4] A.A. Kilbsa, H. M. Srivastava, J.J. Trujillo. Theory and Applications of
Fractional Dierential Equations, Elsevier, Amsterdam, 2006.
[5] S. Q. Zhang, Existence results of positive solutions to boundary value
problem for fractional dierential equation, ,Positivity 13(2009), 583-599.
[6] S. Zhang, The existence of a positive solution for a nonlinear fractional
dierential equation, J. Math. Anal. Appl. 252 (2000), 804-812.
[7] S. Zhang, Positive solution for some class of nonlinear fractional
dierential 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 dierential 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.