Fractional Sturm-Liouville Equations: Self-Adjoint Extensions

摘要

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.