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The existence of a positive solution for a nonlinear fractional differential equation. (English) Zbl 0972.34004
Summary: The author proves existence and uniqueness theorems on a nonlinear fractional differential equation.

##### MSC:
 34A25 Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.) 26A33 Fractional derivatives and integrals (real functions) 34A34 Nonlinear ODE and systems, general
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##### References:
 [1] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equation. (1993) · Zbl 0789.26002 [2] Campos, L. M. C.M: On the solution of some simple fractional differential equations. Internat. J. Math. sci. 13, 481-496 (1990) · Zbl 0711.34019 [3] Ling, Y.; Ding, S.: A class of analytic functions defined by fractional derivative. J. math. Anal. appl. 186, 504-513 (1994) · Zbl 0813.30016 [4] Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation. J. math. Anal. appl. 204, 609-625 (1996) · Zbl 0881.34005 [5] Zhong, Chengkui; Fan, Xianlin; Chen, Wenyuan: Nonlinear functional analysis and its application. (1998) [6] Li, Fuyi; Fen, Jinfeng; Shen, Penlong: The fixed point theorem and application for some decreasing operator. J. math. 42, 193-196 (1996) [7] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in order Banach space. SIAM rev. 18, 620-709 (1976) · Zbl 0345.47044