On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians

TL;DR

This paper establishes bounds on the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians of different orders, with applications across various scientific fields.

Contribution

It introduces new bounds for eigenvalue sums in problems with mixed fractional operators, expanding understanding of their spectral properties.

Findings

Existence of a sequence of eigenvalues for the problem.

Derived lower and upper bounds for the sum of eigenvalues.

Applications demonstrated in medicine, plasma physics, and population dynamics.

Abstract

In this paper, we show the existence of a sequence of eigenvalues for a Dirichlet problem involving two mixed fractional operators with different orders. We provide lower and upper bounds for the sum of the eigenvalues. Applications of mixed fractional operators with different orders include medicine, plasma physics, and population dynamics.