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

Authors: 

Ngo Van Hoa, Nguyen Dinh Phu

Source title: 
Advances in Difference Equations, 2013:290, 2013 (ISI)
Academic year of acceptance: 
2013-2014
Abstract: 

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.