Discrete fractional calculus and obtaining explicit solutions for legendre equation

Fractional and discrete 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 nabla operator of the discrete fractional calculus. In this thesis; firstly, obtaining the general solutions of linear difference equaitons of fractional order with constant coefficients is mentioned. Later, particular solutions of homogeneous and non-homogeneous Legendre differential equation and associated Legendre equation with singular points are obtained with the help of discrete fractional calculus. Keywords: Fractional Calculus, Discrete Fractional Calculus, Differential Equations of Fractional Order,Legendre Differential Equation, Associated Legendre Equation