Solutions of the generalized Laguerre differential equation with the help of fractional differintegral

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, definition, theorems and properties of fractional analysis are mentioned. Then, the Schrödinger equation, witch is the time-independent in the fields of physics and engineering, is considered. These type equations are linear and secondorder partial differential equations. Separation of variables, Green's functions, and integral transforms are among the most frequently used techniques for obtaining their analytic solutions. In this study, the equations provided by angular and radial part are obtained by using the method of separating variables in the spherical coordinates. In the equation provided by the radial part, Laquerre differential equation was obtained by making appropriate transformations. Later particular solutions of homogeneous and non-homogeneous Laquerre differential equation with singular points are obtained with the help of fractional analysis. Keywords: Fractional differintegral, Fractional analysis, Laquerre equation