Identification of an unknown source term for a time fractional fourth-order parabolic equation

Abstract

In this article, we considered two inverse source problems for fourth-order parabolic differential equation with fractional derivative in time. Determination of a space dependent source term from the data given at some time t=T is considered in one problem while other addresses the recovery of a time dependent source term from the integral type over-determination condition. Existence and uniqueness of the solution of both inverse source problems are proved. The stability results for the inverse problems are presented.

Keywords

• Inverse problem
• fractional derivative
• integral equation
• Riesz basis
• bi-orthogonal system of functions
• Fourier series