Approximate solutions of Legendre’s differential equation by using fractional differential transform method

In this article, we examine the fractional order of Legendre’s equations by applying the Differential Transformation Method (DTM). This method is effective and sustainable in the investigation of Legendre’s equations. Series solution could be used to compare the Bessel and Legendre differential equations. If α = 1 then, to get the solution of fractional order of Legendre’s equation. Generalized fraction variation will use to calculate the fraction form of a special function. The results of the Legendre equation will compare with the exact solutions at α=1 and also shows that the method is quite precise and reliable.