Fractional Operators in the Matrix Variate Case

TL;DR

This paper explores fractional integral operators involving matrix arguments, focusing on hypergeometric functions, their properties, and applications in modeling complex natural science problems with flexible functional pathways.

Contribution

It introduces new fractional integral operators for matrix variate hypergeometric functions and incorporates the pathway idea to connect various functional forms.

Findings

Derived properties and limiting forms of fractional operators

Introduced pathway concept for flexible modeling

Applied to natural science problems for optimal solutions

Abstract

Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric function with the argument being a rectangular matrix. Subsequently some fractional integral operators are introduced which complement these results available on fractional operators in the matrix variate cases. Several properties and limiting forms are derived. Then the pathway idea is incorporated to move among several different functional forms. When these are used as models for problems in the natural sciences then these can cover the ideal situations, neighborhoods, in between stages and paths leading to optimal situations.