Explicit solutions of a certain class of associated Legendre equations by means of fractional calculus

摘要

In recent years, many authors have demonstrated the usefulness of fractional calculus in the derivation of particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders. The main object of the present paper is to show how several recent contributions on this subject, involving a certain class of associated Legendre equations, can be obtained (in a unified manner) by suitably applying some general theorems on particular solutions of a certain family of linear ordinary fractional differintegral equations.