星图上的一类非线性Caputo序列分数阶微分方程边值问题解的存在性

doi:10.6040/j.issn.1671-9352.0.2020.668

摘要/Abstract

摘要： 研究了一类定义在由3个节点和两条边构成的星图上的非线性Caputo类型的序列分数阶微分方程边值问题(boundary value problem, BVP)解的存在性。通过变量变换,将所研究的带混合边界条件具有不同定义域的分数阶微分方程组转化为等价的具有相同定义域的带同等边界条件的微分方程组。然后借助Schaefer和Schauder不动点定理得到了边值问题解存在的充分条件,借助Banach不动点定理得到了边值问题解存在且唯一的充分条件。

关键词: 分数阶微积分, 星图上的微分方程, 边值问题, 格林函数

Abstract: The existence of solutions for a class of nonlinear Caputo type sequential fractional differential equations BVP on a star graph consisting of three nodes and two edges is investigated. By using variable transformation, the system of fractional differential equations, with mixed boundary conditions and the different domain, is transformed into an equivalent system of differential equations with the same boundary conditions and domain. Then, by using Schaefer fixed point theory and Schauder fixed point theory, a sufficient condition is obtained for the existence of solutions to boundary value problems, and by means of Banach fixed point theory, a sufficient condition is obtained for the existence and uniqueness of solutions to boundary value problems.

Key words: fractional calculus, differential equations on star graph, boundary value problem, Greens function

中图分类号:

O175.14

李宁,顾海波,马丽娜. 星图上的一类非线性Caputo序列分数阶微分方程边值问题解的存在性[J]. 《山东大学学报(理学版)》, 2022, 57(7): 22-34.

LI Ning, GU Hai-bo, MA Li-na. Existence of solutions for boundary value problems of a class of nonlinear Caputo type sequential fractional differential equations on star graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(7): 22-34.

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