一类具有Caputo导数的非线性分数阶微分方程耦合系统的正解

Abstract

本文研究了一类非线性分数阶微分方程耦合系统的正解存在性，此耦合系统具有Caputo导数和边界条件。通过运用一个新的研究具有矢量的算子的不动点方法，Krasnoselskii锥不动点定理，得到系统的正解存在性。进一步拓展定理得到正解的局限性和多重性。 In this paper, we study the existence of positive solutions for a class of nonlinear coupled system of fractional-order differential equations with Caputo derivatives and boundary conditions. By using a new method to study the fixed points of operators with vectors, Krasnoselskii fixed point theorem of cone, the existence of positive solutions of the system is obtained. We also investigate the localization and multiplicity of the positive solutions by further extending the theorem.