Spectral properties of fractional differentiation operators

Abstract

We consider the fractional differentiation operators in a variety of senses. We show that the strong accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for operators second order with fractional derivative in lower terms, we explore the location of spectrum and resolvent sets and show that the generalized spectrum is discrete. We prove that there is two-sided estimate for eigenvalues of real component of operators second order with fractional derivative in lower terms.

Keywords

• Fractional derivative
• fractional integral
• energetic space
• sectorial operator
• strong accretive operator