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

Abstract

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 and integration, 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.

Keywords

• Inverse problem
• Bi-flux equation
• Fourier method
• Conjugate gradient method

Supporting Institution

none

References

1. [1] M. Alosaimi, I. Tekin, I. and M.A. Çetin, Restoration of the merely time-dependent lowest term in a linear Bi-flux diffusion equation, Comput. Appl. Math. 43 (8), 417, 2024