Series decomposition of a class of special integrals

TL;DR

This paper introduces a novel method for calculating a specific class of integrals, enabling the derivation of optimal bounds for nonlocal evolution equations.

Contribution

The paper presents a new integral calculation technique that simultaneously provides upper and lower bounds for a class of nonlocal evolution equations.

Findings

Method yields both upper and lower bounds simultaneously.

Applicable to a special class of integrals and nonlocal evolution equations.

Enhances existing techniques with improved bounds.

Abstract

In this paper, we propose a new method for calculating integrals for a special class of integrands. As an application, we show how this method can be used to derive optimal pointwise temporal estimates for a class of nonlocal evolution equations. Compared with other methods, our approach can obtain both upper bound and lower bound simultaneously.