The Pantograph Equation in Quantum Calculus

摘要

In this thesis, the pantograph equation in quantum calculus is investigated. The pantograph equation is a famous delay differential equation that has been known since 1971. Till the present day, the continuous and the discrete cases of the pantograph equation are well studied. This thesis deals with different pantograph equations in quantum calculus. An explicit solution representation and the exponential behavior of solutions of a pantograph equation are proved. Furthermore, several pantograph equations regarding asymptotic stability are considered. In fact, conditions for the asymptotic stability of the zero solution are derived and subsequently illustrated by examples. Moreover, an explicit solution in terms of the exponential function for a special pantograph equation is obtained.