Unique iterative positive solutions for a singular p-Laplacian fractional differential equation system with infinite-point boundary conditions

Abstract

By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green's function is derived and some useful properties of the Green's function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the positive solutions for the boundary value problem are established. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, μ, and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.

Multiple positive solutions for singular higher-order semipositone fractional differential equations with p-Laplacian

“…If u ∈ ∂(K e5 ), then u = e 5 and (e 3 /(α−1))t α−1 (e 5 /(α−1))t α−1 u(t) e 5 , t ∈ [0, 1]. Thus, (15) holds. By (15), (A3), Lemmas 4 and 5, similar to the proof of (16), for any n > N 1 , one gets…”

Explicit monotone iterative sequences for positive solutions of a fractional differential system with coupled integral boundary conditions on a half-line

“…In particular, a monotone iterative technique is believed to be an efficient and important method to deal with sequences of monotone solutions for initial and boundary value problems. For some applications of this method to nonlinear fractional differential equations, see [16][17][18][19][20][21][22][23][24]. We also note that there are some results about monotone iterative solution of a single fractional order equation on a half-line, see [25][26][27][28][29].…”

Existence and uniqueness of solutions for a class of higher-order fractional boundary value problems with the nonlinear term satisfying some inequalities

“…Furthermore, the condition that the nonlinearity contains the derivative of the unknown function, especially the fractional-order derivative, causes some mathematical difficulties but make the research very interesting. We refer to [19,21,25,27,29,37,44,50,59,61]. For instance, in [21] the authors investigated the following fractional boundary value problem:…”