An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

Abstract

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

Keywords

• subdiffusion equation
• inverse source problem
• Riesz basis
• Mittag–Leffler function
• Stieltjes function