Journal of the Australian Mathematical Society

Table of Contents - 1972 - Volume 14, Issue 04  

Research Article

Two index laws for fractional integrals and derivatives

E. R. Lovea1

a1 Department of Mathematics The University of Melbourne Victoria, 3052 Australia

Summary

The first index law, or addition theorem, is well known. The second is much less well known; but both have been found to be of importance in recent studies of hypergeometric integral equations. The first law has usually been considered only in the simple case of orders of integration which have positive real part, or in the context of generalized functions. Arising out of the need to manipulate expressions involving several fractional integrals and derivatives, our aim here is to establish both laws for all combinations of complex orders of integration and differentiation, and for nearly all functions for which the fractional derivatives involved exist as locally integrable functions.

(Received February 27 1970)