# Abstract Fractional Calculus for m-accretive Operators

## TL;DR

This paper develops an abstract framework for fractional differential operators, exploring their spectral properties and generalizations, with implications for understanding complex differential operators via semigroup theory.

## Contribution

It introduces a new operator class $rak{G_{eta}}$, generalizes transforms of m-accretive operators, and analyzes their spectral characteristics.

## Key findings

- Defined the operator class $rak{G_{eta}}$
- Analyzed spectral properties of fractional operators
- Extended the theory of m-accretive operators

## Abstract

In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators in terms of the infinitesimal generator of a corresponding semigroup. We study such operators as a Kipriyanov operator, Riesz potential, difference operator. Along with this, we consider transforms of m-accretive operators as a generalization, introduce an operator class $\mathfrak{G_{\alpha}}$ and provide a description of its spectral properties.