Based on Gradient Algorithm for the Inverse Source Problem of a Class of Time-space Fractional Diffusion Equations

Abstract

Since entering the 21st century, the establishment of fractional-order diffusion equations in various fields has been of great value and has garnered widespread attention. This study focuses on inverse source term problem for time-space fractional diffusion equation (TSFDE) using given boundary data. First, the identification source problem is transformed into a functional minimization problem utilize the Tikhonov-type regularization method. Then, the sensitivity and the adjoint problem are derived, and the gradient of functional is obtained. The conjugate gradient algorithm is used to solve the minimization problem. Finally, three xamplel with different types of source terms are used to stated the effectiveness and stability, the impact of various parameters on the numerical results is analyzed.