Computing the matrix Mittag-Leffler function with applications to fractional calculus
arXiv:1804.04883 · doi:10.1007/s10915-018-0699-5
Abstract
The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of derivatives of possible high order depending on the matrix spectrum. Regarding the ML function, the numerical computation of its derivatives of arbitrary order is a completely unexplored topic; in this paper we address this issue and three different methods are tailored and investigated. The methods are combined together with an original derivatives balancing technique in order to devise an algorithm capable of providing high accuracy. The conditioning of the evaluation of matrix ML functions is also studied. The numerical experiments presented in the paper show that the proposed algorithm provides high accuracy, very often close to the machine precision.
References in corpus (7)
- Numerical evaluation of two and three parameter Mittag-Leffler functions
- The Prabhakar or three parameter Mittag--Leffler function: theory and application
- Models of dielectric relaxation based on completely monotone functions
- Prabhakar-like fractional viscoelasticity
- Global Padé approximations of the generalized Mittag-Leffler function and its inverse
- Storage and dissipation of energy in Prabhakar viscoelasticity
- Time-Optimal Control of Linear Fractional Systems
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