Arbitrary real-order cost functions for signals and systems

This work focuses on a new type of cost function based on fractional operators. To do so, the concept of definite integral is extended to arbitrary real-order. Some properties of this new fractional-order definite integral are studied and a fractional-order Barrow's rule is proposed. It is illustrated by an example (the design of an IIR filter) how this new kind of cost function can be a valuable tool in problems where optimal design methods are involved.