On boundary-value problems for a partial differential equation with Caputo and Bessel operators

TL;DR

This paper studies the unique solvability of boundary-value problems for a time-fractional PDE involving Caputo and Bessel operators, providing explicit solutions using spectral expansion and special functions.

Contribution

It introduces explicit solution formulas for direct and inverse problems with Caputo and Bessel operators using spectral expansion methods.

Findings

Explicit solutions expressed via Mittag-Leffler and Bessel functions

Proved unique solvability of the formulated problems

Applied spectral expansion to fractional PDEs with special operators

Abstract

In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of solutions to formulated problems in terms of multinomial Mittag-Leffler and first kind Bessel functions.