A fractional calculus operators approach to doubly confluent Heun and generalized ellipsoidal wave equations

Operators of fractional calculus, which deals with differentiation and integration of arbitrary order, have been used recently to solve various types of differintegral equations. In this paper we consider a second order non-homogeneous differential equation, and obtain its particular solution by an appeal to the operators of fractional integration. Doubly confluent Heun equations and generalized ellipsoidal wave equations can be recovered from the general theorem established here. Several other special cases with their particular solutions are mentioned.