LAUSR

In this report we study a fractional analogue of Sturm–Liouville equation. A class of self-adjoint fractional Sturm–Liouville operators is described. We give a biological interpretation of the fractional order equation and nonlocal boundary conditions that arise in describing the systems separated by a membrane. In particular, the connection with so called “fractional kinetic” equations is observed. Also, some spectral properties of the fractional kinetic equations are derived. An application to the anomalous diffusion of particles in a heterogeneous system of the fractional Sturm–Liouville equations is discussed.