Abstract
We present an efficient numerical solution for the fractional inverse parabolic problem with an unknown condition in this study. In addition to the unknown temperature function, the suggested fractional inverse parabolic problem also has an unknown boundary condition. To tackle the two independent variables, the suggested system employs a fully spectral collocation approach. Some numerical examples were supplied for demonstration purposes to demonstrate the numerical methods’ asymptotic behaviour. The results indicate that our spectral collocation method is more flexible and accurate than previous methods. It also verified the spectral scheme’s exponential convergence.