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Green’s formula for integro-differential operators. (English) Zbl 1486.47085

Summary: In this report we establish Green’s formula for an integro-differential operator, and apply it to describe a class of self-adjoint fractional order differential operators. A found symmetric fractional order Caputo-Riemann-Liouville type operator can be considered as a fractional analogue of the classical Sturm-Liouville operator in some sense.

MSC:

47G20 Integro-differential operators
45J05 Integro-ordinary differential equations
34B24 Sturm-Liouville theory
34A08 Fractional ordinary differential equations
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