Affiliations: [a]
Department of Mathematics, College of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, P.R. China | [b]
Department of Big Data Science and Engineering, College of Big Data and Information Engineering, Guizhou University, Guiyang, Guizhou, P.R. China
Correspondence:
[*]
Corresponding author. Zhuhong Zhang, Department of Big Data Science and Engineering, College of Big Data and Information Engineering, Guizhou University, Guiyang, Guizhou 550025, P.R. China. Tel.: +86 851 83629086; E-mail: zhzhang@gzu.edu.cn.
Abstract: This work investigates the continuous dependence, global existence and stability theory of mild solutions for a class of semi-linear interval-valued differential equations under gH-differentiability. Some basic integral properties are developed by generalizing the conventional concept of interval integral for interval-valued functions. The acquired properties, along with a new comparison theorem in interval-valued environments, ensure that the solutions of such kind of equations depend continuously on the initial state and also the nonlinear disturbance term under certain assumptions. The global existence of such solutions is established under gH-differentiability, relying upon solution extension and the Cauchy convergence criterion. Several concepts of stability are introduced to study the stability of interval dynamic systems in terms of another new comparison theorem and a Lyapunov-like function, which draws that the zero point is exponentially stable.
Keywords: gH-derivative, interval-valued Cauchy problem, continuous dependence, global existence, stability
