Space-Time Caputo Fabrizio Fractional Differentiation through a Proposed Fixed Transform-Based Domain (Ftd) Approach for Groundwater Model

Mathematical models of groundwater flow have been used since the late 1800s. A set of differential equations known to control groundwater flow make up a mathematical model. We suggest the Fixed Transform Domain (FTD) approach to address the Ground Water Flow Problem's Time-space Fractional derivative. The fractional differential equation can represent groundwater flow since it is not static and can relate to initial and boundary circumstances. Utilizing the Darcy law and the conservation of mass law, this model considers the water flow to the piezometric head as a function of the derivative of the fractional arrangement. The primary goal of this study was to provide a novel idea for simulating issues with groundwater flow. Finally, two cases and simulations for these examples show that the proposed method works. Empirical instances demonstrate that the suggested approach is highly efficient and applicable to related issues. A numerical scheme stability analysis is provided to confirm the effectiveness of the proposed framework. By comparing the results of the suggested method with those of Barker's fractal radial flow framework, an association between the non-integral dimension of the flow and the fractional order of the derivative is illustrated. Additionally, the proposed method is highly effective and applicable to similar problems.