The spectral properties of fractional order differential operators

The concept of fractional order derivatives has been studied for a long time. The reason for this is that integer order derivatives are thought to be insufficient to explain physical events, will be better expressed with a fractional order derivative, and will give better results. The most commonly used fractional calculus types are Riemann-Liouville's and Caputo's fractional derivatives and integrals. In this study, first the approaches and solution proposals in these fields are emphasized, and then this Sturm-Liouville boundary value problem is studied. Especially, some important theorems in classical Sturm-Liouville theory are considered for the fractional case.