A Table of Derivatives on Arbitrary Time Scales
Delfim F. M. Torres
TL;DR
This paper systematically compiles formulas for derivatives on arbitrary time scales and introduces generalized trigonometric and hyperbolic functions that preserve key properties of their continuous counterparts.
Contribution
It provides a comprehensive collection of dynamic derivative formulas on time scales and defines generalized trigonometric and hyperbolic functions with preserved properties.
Findings
Collected formulas of derivatives on arbitrary time scales
Defined generalized trigonometric and hyperbolic functions
Preserved qualitative properties of classical functions
Abstract
This paper presents a collection of useful formulas of dynamic derivatives on time scales, systematically collected for reference purposes. As an application, we define trigonometric and hyperbolic functions on time scales in such a way the most essential qualitative properties of the corresponding continuous functions are generalized in a proper way.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Matrix Theory and Algorithms · Advanced Differential Equations and Dynamical Systems