Abstract <p>It is proposed for the first time to use non-integer order moments for the analysis of the sorption kinetics of gases and liquids by membranes and adsorbents. An analytical formula for the moment of the gas sorption kinetic curve by a homogeneous membrane of any non-negative order has been obtained. It is shown that the first and second order moments obtained using this formula coincide with known analytical expressions for these moments. An expression has been derived for calculating the diffusion coefficient using a non-integer order moment. Through mathematical modeling, it has been demonstrated that the error in determining the diffusion coefficient depends on the total measurement time of the sorption kinetic curve and the order of the kinetic curve moment.</p>