关键词: 分数阶微分方程, 无穷区间, 积分边值问题, L¹-Carathéodory条件, 不动点定理

Abstract: We considered  integral boundary value problem of a class of Riemann-Liouville fractional differential equations with multiple fractional derivative terms on infinite intervals. By constructing a new Banach space and using the nonlinear analysis theory, and under the condition that the nonlinear term satisfied the L¹-Carathéodory conditions, some conclusions  for existence and uniqueness of positive solutions to boundary value problems were obtained, and an example was used to illustrate the applicability and universality of the obtained results.

Key words: fractional differential equation, infinite interval, integral boundary value problem,  , L¹-Carathéodory condition, fixed point theorem