Generalized Weber Equations via Fractional Calculus

Abstract

Based on Nishimoto's fractional calculus [1], the particular solutions to the well-known special second order differential equations, such as Gauss, Legendre, Jocobi, Tchebycheff, and Coulomb have been obtained. As for their generalized form, their particular solutions are discussed via fractional calculus method by some authors ([2]~[7]). Recently, in 1999, S.T.Tu, et al. [8] have treated the particular solution to the generalized Nth order equations, such as Associated Legendre, Euler, and Hermite equations. In 1998, K. Nishimoto [10], obtaincd a particular solution to the famous second order Weber cquation which appeared in quantum mechanics by using his N' method. In this paper, the solution to its generalized Weber equation by using fractional calculus method will be discussed in detail with some examples given.