Stability estimate for identification of the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators

Key Points

• This research aims to establish a stability estimate for identifying unknown parameters in time fractional diffusion equations.
• Development of a Hölder-type stability estimate.
• Application to time fractional diffusion equations with local and nonlocal operators.
• Mathematical derivation of conditions for stability.
• First stability estimate result for the identification problem is presented.
• Illustrates improved identification accuracy under specified conditions.