Solution of conformable Laguerre and associated Laguerre equations using Laplace transform†

In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series method. In addition some properties and some recursion relations of the Laguerre and associated Laguerre functions are discussed and proved. Then, the conformable Rodriguez's formula and generating function are propose