Multiple Unbounded Positive Solutions for the Boundary Value Problems of the Singular Fractional Differential Equations

- Journal title : Kyungpook mathematical journal
- Volume 53, Issue 2, 2013, pp.257-271
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2013.53.2.257

Title & Authors

Multiple Unbounded Positive Solutions for the Boundary Value Problems of the Singular Fractional Differential Equations

Liu, Yuji; Shi, Haiping; Liu, Xingyuan;

Liu, Yuji; Shi, Haiping; Liu, Xingyuan;

Abstract

In this article, we establish the existence of at least three unbounded positive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.

Keywords

Positive solution;fractional differential equation;fixed-point theorem;

Language

English

References

1.

R. P. Agarwal, M. Benchohra and S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl Math, 109(2011), 973-1033.

2.

A. Arara, M. Benchohra, N. Hamidi and J. J. Nieto, Fractional order differential equations on an unbounded domain, Nonlinear Analysis TMA, 72(2010), 580-586,

3.

Z. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Analysis, 72(2010), 916-924.

4.

R. Dehghant and K. Ghanbari, Triple positive solutions for boundary value problem of a nonlinear fractional differential equation, Bulletin of the Iranian Mathematical Society, 33(2007), 1-14.

5.

A. A. Kilbas and J. J. Trujillo, Differential equations of fractional order: methods, results and problems-I, Applicable Analysis, 78(2001), 153-192.

6.

R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana University Mathematics Journal, 28(1979), 673-688.

7.

Y. Liu, Positive solutions for singular FDES, U.P.B. Sci. Series A, 73(2011), 89-100.

8.

K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, Wiley, New York, 1993.

9.

S. Z. Rida, H. M. El-Sherbiny and A. A. M. Arafa, On the solution of the fractional nonlinear Schrodinger equation, Physics Letters A, 372(2008), 553-558.

10.

S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integral and Derivative. Theory and Applications, Gordon and Breach, 1993.

11.

X. Xu, D. Jiang and C. Yuan, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Analysis TMA, 71(2009), 4676-4688.

12.

F. Zhang, Existence results of positive solutions to boundary value problem for fractional differential equation, Positiviyt, 13(2008), 583-599.