Inverse problem for recovery of temporal component of source term for multi-term time fractional parabolic equation with nonlocal boundary datum

TL;DR

This paper investigates an inverse problem for a multi-term fractional parabolic equation with nonlocal boundary conditions, using spectral analysis and special functions to establish solution properties.

Contribution

It introduces a novel approach to solve inverse problems involving multi-term fractional derivatives with nonlocal boundary conditions using bi-orthogonal systems.

Findings

Established the classical nature of solutions under regularity conditions

Developed a solution construction involving double infinite series

Analyzed spectral properties of the non-self-adjoint problem

Abstract

Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral problem. A bi-orthogonal system of functions is used to construct the solution that involves double infinite series. Properties of multinomial Mittag-Leffler function and eigenfunctions are used to prove the classical nature of the solution under certain regularity conditions on the given datum.