Semi-linear diffusive representations for non-linear fractional differential systems

Abstract

The stability of non-linear fractional differential equations is studied. A sufficient stability condition on the non-linearity is given for the input-output stability, thanks to many different reformulations of the system using diffusive representations of dissipative pseudo-differential operators. The problem of asymptotic internal stability is analyzed by a more involved functional analytic method. Finally, a fractional version of the classical Hartman-Grobman theorem for hyperbolic dynamical systems of order 1 is conjectured and reformulated, based upon known necessary and sufficient stability conditions for linear fractional differential equations.