Proportional dynamic systems

In the first part of this study, the place and importance of proportional derivative in the literature is given. In the second part the proportional derivative and its main properties on the time scale are given, and the basic definitions and theorems that will be used throughout the thesis are defined. In the third chapter, proportional dynamic systems and their solutions on time scales are examined. In the fourth chapter, linear time-varying dynamic-algebraic equations are given in detail. The last chapter is the original part of the study, and in this chapter, linear time-varying dynamical-algebraic equations are obtained in terms of proportional derivatives and their equivalent systems are found.