A certain family of fractional differintegral equations

In recent years, several workers demonstrated the usefulness of fractional calculus in the derivation of particular solutions of a number of familiar second-order differential equations associated (for example) with Gauss, Le gendre, Jacobi, Chebyshev, Coulomb, Whittaker, Euler, Hermite, and Weber eq uations. The main object of this paper is to show how some of the most rece nt contributions on this subject, involving the Weber equations and their v arious generalized forms, can be obtained by suitably applying a general th eorem on particular solutions of a certain family of fractional differinteg ral equations.