ABSTRACT
The exact solution of every differential solution dose not exists though it is of integer order, and then there is need to turn toward the numerical solution or series solution. The same is the case with fractional order differential equation, likewise differential equations; series solutions also exist for the fractional ordered differential equations. This chapter studies the fractional power series solution of Laguerre and Chebyshev conformable differential equations using Katugampola's derivative which is the generalized form of conformable derivative. Existence and uniqueness theorem of linear conformable fractional differential equations around a point has been given and the existence of fractional power series solutions about a singular point of sequential conformable differential equation have been presented. The findings of the whole work indicate that the results of the fractional case conform with the results of the ordinary case.
