Mittag-Leffler function

APPLICATION OF FRACTIONAL ORDER DIFFUSION MODEL IN ANALYSIS OF DIFFUSION-WEIGHTED MAGNETIC RESONANCE IMAGING DATA

This study explores the application of a fractional diffusion equation in diffusion-weighted magnetic resonance imaging (DW-MRI or DWI) analysis, aiming to validate and extend previous research based on an open-access dataset. A fractional-order model using the Mittag-Leffler function is implemented and validated by reproducing results presented in existing literature. The method is then applied to an open-access Connectome Diffusion Microstructure Dataset (CDMD) to analyze real brain imaging data.

Thermal stresses in a long cylinder under Gaussian-distributed heating in the framework of fractional thermoelasticity

An axisymmetric problem for Gaussian-distributed heating of a lateral surface of an infinite cylinder is solved in the framework of fractional thermoelasticity based on the time-fractional heat conduction equation with the Caputo derivative. The representation of stresses in terms of displacement potential and Love function is used to satisfy the boundary conditions on a surface of a cylinder. The results of numerical calculation are presented for different values of the order  of fractional derivative and nondimensional time.