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On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation

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  • Marina Popolizio

    (Department of Electrical and Information Engineering, Polytechnic University of Bari, Via E. Orabona n.4, 70125 Bari, Italy
    INdAM Research Group GNCS, Istituto Nazionale di Alta Matematica “Francesco Severi”, Piazzale Aldo Moro 5, 00185 Rome, Italy)

Abstract

Many situations, as for example within the context of Fractional Calculus theory, require computing the Mittag–Leffler (ML) function with matrix arguments. In this paper, we collect theoretical properties of the matrix ML function. Moreover, we describe the available numerical methods aimed at this purpose by stressing advantages and weaknesses.

Suggested Citation

  • Marina Popolizio, 2019. "On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation," Mathematics, MDPI, vol. 7(12), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1140-:d:289628
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    References listed on IDEAS

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    1. Sadeghi, Amir & Cardoso, João R., 2018. "Some notes on properties of the matrix Mittag-Leffler function," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 733-738.
    2. Del Buono, N. & Lopez, L. & Politi, T., 2008. "Computation of functions of Hamiltonian and skew-symmetric matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1284-1297.
    3. Garrappa, Roberto & Popolizio, Marina, 2011. "On the use of matrix functions for fractional partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1045-1056.
    4. Politi, Tiziano & Popolizio, Marina, 2015. "On stochasticity preserving methods for the computation of the matrix pth root," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 53-68.
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    Cited by:

    1. Kataria, K.K. & Khandakar, M., 2022. "Extended eigenvalue–eigenvector method," Statistics & Probability Letters, Elsevier, vol. 183(C).
    2. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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