q-differential equations of first order

In this thesis, the solutions of homogeneous and non-homogeneous parts of the first order q-differential equations with constant and variable coefficient have been investigated in Hilbert space. Then the results have been compared with the results already known in classical analysis. In the first chapter, a brief history of analysis and q-analysis is given. In the second chapter, the basic concepts and well known results of differential equations, operator theory and q-analysis which we need have been recalled. In the third chapter, the problems mentioned above have been investigated. Moreover, all results in this thesis have been supported with examples.