Green's Theorem for Generalized Fractional Derivatives

TL;DR

This paper extends Green's theorem to a broader class of generalized fractional derivatives with more flexible kernels, providing new theoretical results even in classical cases.

Contribution

It introduces an extension of Green's theorem for generalized partial fractional derivatives with more general kernels, expanding the mathematical framework.

Findings

Extended Green's theorem for generalized fractional derivatives.

Derived new results in classical fractional calculus cases.

Established theoretical foundations for future research in fractional analysis.

Abstract

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.