Mahouton Norbert Hounkonnou
Discrete mechanics in non-uniform time $\alpha$-lattices
In this talk, we consider special types of non-uniform time lattices by introducing the $\alpha$-addition and $\alpha$-subtraction from the point of view of pseudo-analysis, a generalization of the classical analysis, where instead of the field of real numbers, a semiring is taken on a real interval $[a, b] \subset [-\infty, +\infty].$ In this framework, we deduce related algebraic operations and discuss their properties. We define the discrete conformable fractional derivative and integral by introducing the fractional falling factorial. We derive the Langevin equation and describe the two-dimensional discrete mechanics. Besides, we introduce the polar coordinate analysis to describe some relevant physical phenomena.
