2025/06/16 by Nathaniel G. Hermann, Hermann, Nathaniel G., M. Shane Hutson +1
Engineering · Mathematics · #35R11 #60G22 #60J60 (Secondary) #60K50 (Primary) #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.2506.14043
openalex publication_date 2025/06/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or through complex mathematical structures (e.g. Fox-H functions). Here, we present a set of analytic solutions to common time fractional diffusion problems, written in terms of Mittag-Leffler and M-Wright functions, as well as generalized fractional error and complementary error functions derived within. We additionally show how time fractional diffusion is a generalization of a two-parameter stretched-time fractional diffusion process. Finally we present a procedure to take canonical solutions to mass transport problems with Fickian diffusion and extend these to systems with anomalous diffusion.