Comparison theorems and asymptotic behavior of solutions of discrete fractional equations

This thesis consist of 5 main chapters. In the first chapter, the process of discrete calculus up to the present and in which areas it is used are explained. In the second chapter, basic definitions and theorems of nabla and delta difference operators are given. In the third chapter, asymptotic behavior of solutions of discrete fractional delta difference and Caputo fractional delta difference operators with the help of Mittag-Leffler function and Laplace transform is investigated. In the fourth chapter, the asymptotic behavior of solutions of the discrete fractional nabla difference and Caputo fractional nabla difference operators is investigated. In the last chapter, linear systems of fractional nabla difference equations are examined. Convolution is given for the fractional nabla difference operator and some results are obtained with the help of discrete transformation.