Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case

Abstract

In this paper, we study a nonlinear third-order multipoint boundary value problem by the monotone iterative method. We then obtain the existence of monotone positive solutions and establish iterative schemes for approximating the solutions. In addition, we extend the considered problem to the Riemann-Liouville-type fractional analogue. Finally, we give a numerical example for demonstrating the efficiency of the theoretical results.

Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable

“…where 0+ and 0+ are the standard Riemann-Liouville derivatives, ≥ 2, 1 ≤ − ≤ − 1, − 1 < ≤ , 0 < recent years, there has been a great deal of research on the existence and/or uniqueness of solution in studying FDEs nonlocal problems for their wide applications in modeling some important physical laws (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16], for instance).…”

“…In [3], the authors were concerned with the existence of monotone positive solutions to the following fractional-order multipoint boundary value problems…”

Existence criteria of solutions for a fractional nonlocal boundary value problem and degeneration to corresponding integer-order case

“…In the last decades, fractional order boundary value problems have also received plenty of attention from many researchers. There are many achievements derived from some fractional equations with various boundary conditions, some recent contribution can be found in [6][7][8][9][10][11][12][13].…”