Adaptive the Dirichlet model of mobile/immobile advection/dispersion in a time-fractional sense with the reproducing kernel computational approach: Formulations and approximations

In this paper, we will first present the TFMIADM with its adequate Dirichlet constraints. Right after that, we will review the formation of that model under the terms and assumptions of the RKHSM computational approach. The solutions and modeling of the utilized model will be discussed based on Caputo's connotation of the partial time derivative. We will present the scores required to construct the appropriate spaces for the method and we will present several theories such as solutions representations, convergence restriction, and order of error. With the use of the Fourier functions expansion rule, the numeric-analytic solutions are expressed by collection sets of orthonormal functions system in A(H) and B(H) spaces. Right after that, we will solve this model in both time and space domains using the algorithms of the method used. Indeed, several drawings and tables that expound on the effectiveness and strength of the approach and its adaptation to the issue reviewed are utilized. In the end, some points of view and highlights are presented side by side with the most important modern references used.