# Time Scale Calculus Research - Discuss with Fellow Researchers

• MHB
• DrWahoo
In summary, The conversation discusses the topic of research on time scales and its potential for future modeling. The participant has a specific interest in applying Hilger's dissertation to financial modeling and is interested in discussing this topic with others. They also provide a link to a PDF for further reading.
DrWahoo
Anyone here do research with time scales (differential equations(dynamic equations) combining both the continuous and discrete). I know its more of a new topic from Hilger, but I think it is a new wave of modeling that will be prevalent in the future. If anyone is interested on the topic or want to discuss some research, that would be amazing. Here is a quick pdf from the German genius and his Hilger's dissertation introducing the topic. http://www.math.unl.edu/~apeterson1/sample_book.pdf

Yes, I do research on time scales. I am currently working on an application of the Hilger's dissertation in the area of financial modeling. Specifically, I am exploring how the concept of time scales can be used to create a more accurate model for stock price movements. I'm interested in exploring how this new approach can improve the accuracy of predictions and provide deeper insight into the market dynamics.

## 1. What is Time Scale Calculus?

Time Scale Calculus is a branch of mathematics that combines the concepts of both continuous and discrete time systems. It deals with the study of functions and differential equations on a "time scale", which can be any arbitrary set of points containing both real numbers and integers. This allows for a more comprehensive understanding of dynamic systems that exhibit both continuous and discrete behavior.

## 2. How is Time Scale Calculus different from traditional calculus?

Traditional calculus deals with continuous functions on the real numbers, while Time Scale Calculus extends this concept to include both real numbers and integers. This allows for a more versatile approach to modeling and analyzing systems that exhibit both continuous and discrete behavior.

## 3. What are some applications of Time Scale Calculus?

Time Scale Calculus has a wide range of applications, including physics, engineering, economics, and biology. It can be used to model and analyze systems that exhibit both continuous and discrete behavior, such as population dynamics, control systems, and financial markets.

## 4. How does Time Scale Calculus relate to other branches of mathematics?

Time Scale Calculus has connections to various other branches of mathematics, such as differential equations, difference equations, and fractal geometry. It also has applications in fields such as dynamical systems and control theory.

## 5. What are some current research topics in Time Scale Calculus?

Some current research topics in Time Scale Calculus include stability and oscillation theory, fractional calculus on time scales, and applications to complex systems. Other areas of interest include numerical methods and qualitative theory for time scale differential equations.

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