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


Supervisor: Başak Karpuz


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.