Solutions of dynamic equations of second order on time scales


Thesis Type: Postgraduate

Institution Of The Thesis: Dokuz Eylul University, Fen Bilimleri Enstitüsü, Mathematics, Turkey

Approval Date: 2023

Thesis Language: English

Student: GİZEM MOLO

Supervisor: Başak Karpuz

Abstract:

First of all, we will give the main definitions, theorems and examples on time scale calculus in this thesis. Secondly, we will present the solutions and properties of first-order dynamic equations. At the same time, we will examine the solutions under specific time scales with applications. Finally, we will introduce new solution techniques for second-order dynamic equations with constant coefficients. We will apply the technique to general form of second-order dynamic equations, and then we will get a familiar form (as in the case of differential equations) of the solution after making some arrangements considering possible cases of the roots of the so-called characteristic parabola. Further, we will give new formulas for the solutions when the characteristic equation has complex roots.