Software Development for Intraparticle Mass Transfer Modeling Using Fractional Differential Equations

The article deals with the process of developing software for the implementation of the fractional analysis apparatus in the field of mathematical modeling, in particular, on the example of the problem of intraparticle mass transfer in a heterogeneous catalytic porous medium. The main stages of constructing a mathematical model based on the use of fractional Caputo derivatives, which allows taking into account the effects of memory and spatial nonlocality inherent in porous and inhomogeneous materials, are highlighted. For the corresponding one-dimensional boundary-value problem, an analytical solution was found using the Fourier and Laplace transform methods. The algorithmic solutions and software implementation of numerical methods based on Python libraries, in particular NumPy and NumFracPy, which provide efficient computations on multidimensional data sets, are described. Attention is paid to the calculation of the Mittag-Leffler function, which is a component of fractional differential equations. The structure of the program complex is presented. A mechanism for passing input parameters through the command line is implemented. The software product has been verified by conducting numerical experiments and analyzing the behavior of the mathematical model under different para­meters. For this purpose, we calculated the values of the function at the test points and compared the results with the calculations in computer algebra systems. It is confirmed that the numerical solutions coincide with the analytical results. The proposed software solution provides increased accuracy and performance of computations, allowing it to be used to analyze complex multifactorial physical systems.