Syed Abbas, Shekhar Singh Negi, Said R. Grace, Ravi P. Agarwal, Chao Wang

Survey on Qualitative Theory of Dynamic Equations on Time Scale

abstract:
The qualitative theory of dynamic equation on time scale has received lots of attention from researchers due to its applicability to various fields. One of the most important aspects is that it unifies the theory of difference equations, differential equations, quantum calculus, and several others. In this article, we discuss the development of this theory along with the main emphasis on a second order dynamic equation. The qualitative properties, especially development in the oscillation theory of such equations, are discussed in detail. Several examples are provided for a better understanding of this topic.

Mathematics Subject Classification: 34N05, 34C10, 26E70

Key words and phrases: Time scale, Hilger's derivative, oscillation