Conjugated-Order Differintegrals

This paper introduces the concept of conjugated-order differintegrals. These are fractional derivatives whose orders are complex conjugates. These conjugate-order differintegrals allow the use of complex-order differintegrals while still resulting in real time-responses and real transfer-functions. Both frequency responses and time responses are developed. The conjugated differintegral is shown to be a useful representation for control design. An example is presented to demonstrate its utility.© 2005 ASME