Convolution operators via orthogonal polynomials

TL;DR

This paper generalizes fractional calculus results using operator theory, enabling application to diverse physical-chemical processes through the development of convolution operators based on orthogonal polynomials.

Contribution

It introduces a novel approach to fractional calculus by formulating convolution operators via orthogonal polynomials, expanding their applicability to practical physical-chemical problems.

Findings

Generalization of fractional calculus results

Development of convolution operators using orthogonal polynomials

Application framework for physical-chemical processes

Abstract

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained technique on practical problems that connected with various physical - chemical processes.