Qu, H. (2013). Positive Solution for Boundary Value Problem of Fractional Dierential Equation. Theory of Approximation and Applications, 10(1), 87-98.

H. Qu. "Positive Solution for Boundary Value Problem of Fractional Dierential Equation". Theory of Approximation and Applications, 10, 1, 2013, 87-98.

Qu, H. (2013). 'Positive Solution for Boundary Value Problem of Fractional Dierential Equation', Theory of Approximation and Applications, 10(1), pp. 87-98.

Qu, H. Positive Solution for Boundary Value Problem of Fractional Dierential Equation. Theory of Approximation and Applications, 2013; 10(1): 87-98.

Positive Solution for Boundary Value Problem of Fractional Dierential Equation

^{}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 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 innite 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.