From partial differential equations of propagative recursive systems to non-integer differentiation. (English) Zbl 1033.35158

Summary: This paper studies the link between non integer differentiation and the class of partial differential equations describing propagative recursive distributed parameter systems. Through an input-output approach, we show that these systems can be characterised by a particular admittance: a continued fraction. After the study of this continued fraction, we give a theorem which highlights the link of the considered class of partial differential equations with non integer differentiation. We show that the non integer order, and only this, imposes frequency behaviour in a well defined interval. Finally, we propose an illustrative example: the characterisation of the behaviour of a hydraulic pipe.


35S05 Pseudodifferential operators as generalizations of partial differential operators
26A33 Fractional derivatives and integrals
93C20 Control/observation systems governed by partial differential equations