Inverse Problems of a Fractional Differential Equation with Bessel Operator

TL;DR

This paper investigates inverse initial and source problems for a time-fractional differential equation involving a Bessel operator, establishing existence, uniqueness, and series solution convergence.

Contribution

It introduces a novel approach using Bessel function series to solve inverse problems with fractional derivatives and Bessel operators.

Findings

Proved existence and uniqueness of solutions.

Developed series solutions with convergence analysis.

Applied Bessel functions for inverse problem solving.

Abstract

Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on series expansions using a set of Bessel functions of order zero. Convergence of the obtained series solutions is also discussed