Solutions of singular differential equations by means of discrete fractional analysis

Fractional calculus, a branch of mathematical analysis, is the generalization of derivative and integral to the non-integer order. It has quite wide application area in science and engineering. Our aim is to obtain particular solutions for the second order linear differential equations with the help of fractional analysis. In this thesis, firstly the history of fractional analysis and the studies on Nabla fractional operator are mentioned. Then, some used definitions and theorems are mentioned. Finally, explicit solutions for a class of homogeneous and nonhomogeneous linear differential equations with singular coefficients are obtained with the help of the nabla fractional operator. Keywords: Gamma function; Nabla fractional operator; Leibniz rule.