1. The study of dynamic equations on time scales is an area of mathematics that deals with the analysis and solutions of differential equations and difference equations on general time scales. A time scale is a general framework that unifies continuous and discrete dynamics, allowing for a unified treatment of differential and difference equations.
2. Non-additive measure theory, also known as non-additive integration theory or set-valued measure theory, is a branch of mathematics that deals with measures that do not satisfy the additively property. In traditional measure theory, measures assign values to sets in a way that is additive, meaning that the measure of the union of disjoint sets is equal to the sum of their individual measures. Non-additive measures generalize this concept by allowing for more flexible and versatile assignment of values to sets.
I am currently working on derivative of function with respect to the non-additive measure, more precisely, a distorted Lebesgue measure, called Sugeno derivative. The Sugeno derivative, also known as the Choquet derivative or fuzzy derivative, is a concept used in fuzzy set theory to define a derivative-like operator for fuzzy functions. It extends the notion of differentiation from classical calculus to fuzzy sets and allows for the analysis and modelling of fuzzy systems.
