Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

TL;DR

This paper investigates initial boundary value problems for a fractional diffusion equation involving a hyper-Bessel operator, establishing solutions, existence, and uniqueness through eigenfunction expansion.

Contribution

It introduces a novel approach to solving fractional diffusion equations with hyper-Bessel operators, including direct and inverse source problems, and provides a framework for existence and uniqueness.

Findings

Solutions constructed via eigenfunction expansion

Existence and uniqueness established for the problems

Solution methods for non-homogeneous fractional equations

Abstract

Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion and results on existence and uniqueness are established. To solve the resultant equations, a solution to a non-homogeneous fractional differential equation with regularized Caputo-like counterpart hyper-Bessel operator is also presented.