NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(13)60044-2

Abstract

Abstract:

In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.

Key words: Fractional differential equations, positive solution, upper and lower solutions, existence and uniqueness, fixed point theorem

CLC Number:

34B15

LI Nan, WANG Chang-You. NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series B, 2013, 33(3): 847-854.

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