Global existence of solutions for interval-valued second-order differential equations under generalized Hukuhara derivative

Advances in Difference Equations

Van Hoa Ngo¹  Dinh Phu Nguyen² 

[1]Division of Applied Mathematics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

[2]Faculty of Mathematics and Computer Science, University of Science, VNU, Ho Chi Minh City, Vietnam

关键词: interval-valued differential equations;    interval-valued second-order differential equations;    generalized Hukuhara derivative;    global existence;   

DOI  :  10.1186/1687-1847-2013-290

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we present a generalized concept of second-order differentiability for interval-valued functions. The global existence of solutions for interval-valued second-order differential equations (ISDEs) under generalized H-differentiability is proved. We present some examples of linear interval-valued second-order differential equations with initial conditions having four different solutions. Finally, we propose a new algorithm based on the analysis of a crisp solution. Some examples are given by using our proposed algorithm. MSC:34K05, 34K30, 47G20.

【 授权许可】

CC BY