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Full-Text Articles in Mathematics
Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert
Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic …
Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
In this work, we formulate the definition of periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. Using the definition of periodicity, we discuss the existence and uniqueness of periodic solutions to a family of linear dynamic equations on isolated time scales. Examples in quantum calculus and for mixed isolated time scales are presented.