Computation of the generalized Mittag-Leffler function and its inverse in the complex plane

By Rudolf Hilfer, Hansjörg Seybold. 2006

151 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/834ee750d4e53dac2c5ab530b505dba8c1000ce6

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In Computer Vision and Pattern Recognition

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Citations in the corpus

Global Padé Approximations of the Generalized Mittag-Leffler Function and its Inverse (2013, methodology): “Hilfer and Seybold [16] reported a simpler algorithm to compute the generalized Mittag-Leffler function than the one in [15].”
Threefold Introduction to Fractional Derivatives (2008, background): “4] It has only recently been calculated numerically in the full complex plane [62, 108].”
Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel (2009, background): “1) and some of its various generalizations have only recently been calculated numerically in the whole complex plane (see, for example, [10,19]).”
Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator (2012, background): “They have only recently been calculated numerically in the full complex plane [17,18].”
The extended Mittag-Leffler function via fractional calculus (2017, background): “In recent years, the researchers [21, 37] have numerically considered the function defined in (1.”
Multi-parametric mittag-leffler functions and their extension (2013, methodology): “[8] (algorithms for the numerical evaluation of the Mittag-Leffler function and package for computation with Mathematica), Hilfer-Seybold [19] (algorithm for extensive numerical calculations for the Mittag-Leffler function in the whole complex plane, based on its integral representations and exponen”
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics (2011, unknown): “up to now no ocial routine exists for the Prabhakar function whereas for the two parameter Mittag-Leer function a number of authors have provided specic routines and/or numerical methods, see e.g. [5, 6, 17, 38, 39, 47, 50]. 4 Conclusions In this revised paper we have presented a quite general mathe”