The Cauchy type problem for interval-valued fractional differential equations with the Riemann-Liouville gH-fractional derivative

Advances in Difference Equations

Yonghong Shen¹ 

[1] School of Mathematics and Statistics, Tianshui Normal University, Tianshui, P.R. China

关键词: generalized Hukuhara difference;    interval-valued function;    interval-valued Riemann-Liouville fractional integral;    Riemann-Liouville gH-fractional derivative;    Cauchy type problem;   

DOI  :  10.1186/s13662-016-0827-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we establish the relationship between the Cauchy type problem for interval-valued fractional differential equations with the Riemann-Liouville gH-fractional derivative and the corresponding interval-valued integral equation. Moreover, we also consider the existence of the solutions to the interval-valued integral equation. Furthermore, we obtain the solutions to the Cauchy type problem under certain conditions.

【 授权许可】

CC BY