The positive properties of Green’s function for three point boundary value problems of nonlinear fractional differential equations and its applications

Positive properties of the Green function for two-term fractional differential equations and its application

“…But they failed to obtain the positive properties similar to that of [12] in form, and given an open problem about positive properties of the Green function, that is, [24, Remark 2.1]. Wang et al [21,22] established some new positive properties of the corresponding Green function, and solved the open problem of [24]. As application, the existence of positive solutions were obtained for a class of fractional m-point BVPs.…”

“…Fractional differential equations (FDE) serve as an excellent instrument for the description of memory and hereditary properties of various materials and processes. Recently, much attention has been paid to the study of boundary value problems (BVP) of fractional differential equation, such as the singular BVP [17,21,33,34], nonlocal BVP [2,5,20,24], semipositone BVP [19,22,23] and resonant BVP [3,4,18,32].…”

“…In [12], the authors discussed some positive properties of the Green function for Dirichlet-type FBVP, and obtained the existence of positive solutions by using the Krasnosel'skii fixed-point theorem. In [24], the authors investigated the following fractional differential equation:…”

Difference equations involving causal operators with nonlinear boundary conditions

“…As an important branch, boundary value problems (see [5,11,12,19]), especially, difference equations with nonlinear boundary value problems have drawn much attention. In 2008, Wang [15] investigated the first-order functional difference problems with nonlinear boundary value conditions, obtained the existence of extremal solutions by using the monotone iterative method.…”

Positive solutions for a class of fractional differential coupled system with integral boundary value conditions

“…For a detailed description of some recent results, we refer the reader to papers [7,10,13] and [15]- [25] and the references therein. Some kinds of methods are presented, such as the Laplace transform method [16], the upper and lower method [27], the Fourier transform method [14], and the Green's function method [13,22], etc.…”