Coefficient identification problem for a time-fractional bi-flux diffusion equation

Fractional calculus has recently emerged as a powerful mathematical framework for modelling complex systems. Despite its mathematically intricate foundation, it serves as a generalization of classical differentiation andintegration, extending these operations to arbitrary, non-integer (fractional) orders. This study investigates the identification of time-dependent coefficient in a time-fractional Bi-flux equation using interior point measurement within the spatial domain, employing the contraction mapping principle and explore numerical solutions by creating numerical algorithms and testing examples.