Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes

Analysis of Hilfer fractional integro-differential equations with almost sectorial operators

We investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove existence results by applying Schauder's fixed point technique. Moreover, we show fundamental properties of the solution representation by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.