No abstract

In this paper, we are interested in the study of the existence of solutions of a class of nonlinear fractional differential equations coupled with Dirichlet boundary conditions. We make an exhaustive study of the sign of Green’s function related to the linear problem and obtain the exact values for which it has the constant sign on its whole square of definition. This constant sign is equivalent to the validity of anti-maximum principles. The existence of solutions is deduced from a recent fixed point theorem valid for operators defined on suitable cones of Banach spaces. Moreover, the method of lower and upper solutions is developed for the non-homogeneous Dirichlet problem.

This paper is devoted to the study of nonlinear fractional differential equation with parameter dependence and integral boundary value conditions. In the paper various existence and multiplicity results for positive solutions are derived depending of different values of the parameter. Some illustrative examples are also discussed.MSC 2010 : Primary 34A08; Secondary 26A33, 34K37