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Far East Journal of Applied Mathematics

where

is the standard Riemann-Liouvill differentiation, and

is continuous.

By using Krasnoselskii’s fixed point theorem and Leggett-Williams’ theorem, some sufficient conditions for the existence of positive solutions to the above boundary value problems are obtained. We remove the condition that the solutions are concave functions. Two examples are given to illustrate the effectiveness of our results.

Far East Journal of Applied Mathematics
Volume 37, Issue 1, Pages 33 - 47 (October 2009)

POSITIVE SOLUTIONS FOR THREE-POINT BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN
Jinhua Wang (P. R. China), Hongjun Xiang (P. R. China) and Zhigang Liu (P. R. China)

Abstract:
In this paper, we consider the existence of positive solutions for three-point fractional differential equation boundary value problems with p-Laplacian

where