Geodesic
POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
QIU , TINGTING 1 ; BAI, ZHANBING2
1 Department of Mathematics, Shandong University of Science and Technology,Qingdao, 266510, PRC.
2 Department of Mathematics, Shandong University of Science and Technology, Qingdao, 266510, PRC.
Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 3, p. 123-131.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We investigate the positive solution of nonlinear fractional differential equation with semi-positive nonlinearity
$ \begin{cases} D^\alpha_{0^+}u(t) + f(t, u(t)) = 0,\,\,\,\,\, 0 t 1,\\ u(0) = u'(1) = u''(0) = 0 \end{cases} $
where $2 \alpha\leq 3$ is a real number, $D^\alpha_{0^+}$ is the Caputo's differentiation, and $f : [0; 1] \times [0, \infty) \rightarrow (-\infty , \infty)$. By use of Krasnosel'skii fixed point theorem, the existence results of positive solution are obtained.
DOI : 10.22436/jnsa.001.03.01
Classification : 34B15, 34B18
Keywords: Fractional differential equation, Positive solution, Fixed-point theorem.

QIU , TINGTING  1 ; BAI, ZHANBING 2

1 Department of Mathematics, Shandong University of Science and Technology,Qingdao, 266510, PRC.
2 Department of Mathematics, Shandong University of Science and Technology, Qingdao, 266510, PRC. 
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QIU , TINGTING ; BAI, ZHANBING. POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION. Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 3, p. 123-131. doi : 10.22436/jnsa.001.03.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.03.01/

[1] Z. B. Bai Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. , Volume 311 (2005), pp. 495-505

[2] Babakhani, A.; V. D. Gejj Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., Volume 278 (2003), pp. 434-442 | DOI

[3] Delbosco, D.; L. Rodino Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., Volume 204 (1996), pp. 609-625

[4] A. M. A. El-Sayed Nonlinear functional differential equations of arbitrary orders, Nonlinear Analysis TMA , Volume 33 (1998), pp. 181-186 | DOI

[5] Gejji, V. D.; A. Babakhani Analysis of a system of fractional differential equations, J. Math. Anal. Appl., Volume 293 (2004), pp. 511-522 | DOI

[6] Kilbas, A. A.; Marichev, O. I.; S. G. Samko Fractional Integral and Derivatives (Theory and Applications), Gordon and Breach, Switzerland, 1993

[7] Kilbas, A. A.; Trujillo, J. J. Differential equations of fractional order: methods, results and problems-I, Applicable Analysis, Volume 78 (2001), pp. 153-192 | Zbl | DOI

[8] Kilbas, A. A.; Trujillo, J. J. Differential equations of fractional order: methods, results and problems-II, Applicable Analysis , Volume 81 (2002), pp. 435-493 | Zbl | DOI

[9] K. S. Miller Fractional differential equations, J. Fract. Calc. , Volume 3 (1993), pp. 49-57

[10] Miller, K. S.; B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993

[11] Zhang, S. Q. The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl., Volume 252 (2000), pp. 804-812 | DOI

[12] S. Q. Zhang Existence of positive solution for some class of nonlinear fractional differential equations, J. Math. Anal. Appl. , Volume 278 (2003), pp. 136-148 | DOI

[13] Yao, Q. L. Existence of positive solution for a third order three point boundary value problem with semipositone nonlinearity, Journal of Mathematical Research Exposition., Volume 23 (2003), pp. 591-596

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