Spectral properties of fractional differentiation operators

Abstract

We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for differential operators second order with a fractional derivative in the final term, we explore a location of the spectrum and resolvent sets and show that the spectrum is discrete. We prove that there exists a two-sided estimate for eigenvalues of the real component of operators second order with the fractional derivative in the final term.