Approximations of the Mittag-Leffler operator function with exponential accuracy and their applications to solving evolutionary equations with fractional time derivative (Q2107794)

This paper focuses primarily on approximations of the Mittag-Leffler operator function with exponential accuracy and their applications to solving evolutionary equations with fractional time derivative. The discretization of the operator Mittag-Leffler function is presented, which is of interest itself and, in addition, represents the solution operator of a PDE similar to the heat-conduction equation with the fractional time derivative and with an abstract operator coefficient \(A\) in the ``spatial part'' of the equation. A representation of the Mittag-Leffler function in the form of a series with products of the Laguerre-Cayley functions of \(t\) and powers of the Cayley transform of \(A\) is considered.