References
- R. P. Agarwal, A propos d'une note de M. Pierre Humbert, C R Acad. Sci. Paris 236 (1953), pp. 2031–2032.
- H. Amsalu and D.L. Suthar, Generalized fractional integral operators involving Mittag-Leffler function, Abstract Appl. Anal. 2018(6) (2018), pp. 1–8.
- B. Baeumer, M. Kovács, M.M. Meerschaert, and H. Sankaranarayanan, Boundary conditions for fractional diffusion, J. Comput. Appl. Math. 336 (2018 jul), pp. 408–424. Available at https://doi.org/https://doi.org/10.1016/j.cam.2017.12.053 Available at https://linkinghub.elsevier.com/retrieve/pii/S0377042718300219.
- M.M. Djrbashian, On the integral representation of functions continuous on several rays (generalization of the Fourier integral) (in Russian), Izv. Akad. Nauk. SSSR Ser. Mat. 18(5) (1954), pp. 427–448.
- M.M. Djrbashian, On the asymptotic expansion of a function of Mittag-Leffler type (in Russian), Akad Nauk Armjan SSR Doklady 19 (1954), pp. 65–72.
- M.M. Djrbashian, Integral Transfororms and Representation of the Functions in the Complex Domain, Nauka. Glav. red. fiz.-mat. lit, Moscow, (in Russian), 1966.
- M.M. Djrbashian, Harmonic Analysis and Boundary Value Problems in the Complex Domain, Birkhuser Basel, Basel, 1993. Available at https://doi.org/https://doi.org/10.1007/978-3-0348-8549-2.
- R. Garrappa, Numerical evaluation of two and three parameter Mittag-Leffler functions, SIAM J. Numer. Anal. 53(3) (2015 jan), pp. 1350–1369. Available at http://epubs.siam.org/doi/https://doi.org/10.1137/140971191.
- R. Garrappa, The Mittag-Leffler fnction. MATLAB central- File Exchange, 2015. file ID: 48154 Available at https://www.mathworks.com/matlabcentral/fileexchange/48154-the-mittag-leffler-function?s_tid=FX_rc1_behav.
- R. Garrappa and M. Popolizio, Computing the matrix Mittag-Leffler function with applications to fractional calculus, J. Sci. Comput. 77(1) (2018), pp. 129–153. Available at https://doi.org/https://doi.org/10.1007/s10915-018-0699-5.
- R. Gorenflo, A.A. Kilbas, F. Mainardi, and S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer Monographs in Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014. Available at http://link.springer.com/https://doi.org/10.1007/978-3-662-43930-2.
- R. Gorenflo, J. Loutchko, and Y. Luchko, Computation of the Mittag-Leffler function Eα, β(z) and its derivative, Fract. Calculus Appl. Anal. 5(4) (2002), pp. 491–518.
- R. Gorenflo, F. Mainardi, and S. Rogosin, Mittag-Leffler function: properties and applications, in Handbook of fractional calculus with applications, Kochubei A, Luchko Y, eds., Vol. 1, Basic theory. Berlin, Boston, De Gruyter, 2019. pp. 269–296. Available at http://www.degruyter.com/view/books/9783110571622/9783110571622-011/9783110571622-011.xml.
- GSL – GNU Scientific Library; Available at http://www.gnu.org/software/gsl/.
- H.J. Haubold, A.M. Mathai, and R.K. Saxena, Mittag-Leffler functions and their applications, J. Appl. Math. 2011 (2011), pp. 1–51. Available at http://www.hindawi.com/journals/jam/2011/298628/.
- R. Hilfer and H.J. Seybold, Computation of the generalized Mittag-Leffler function and its inverse in the complex plane, Integral Transforms Special Funct. 17(9) (2006 sep), pp. 637–652. Available at http://www.tandfonline.com/doi/abs/https://doi.org/10.1080/10652460600725341.
- P. Humbert, Quelques résultats rélatifs à la fonction de Mittag-Leffler, C R Acad. Sci. Paris 236 (1953), pp. 1467–1468.
- P. Humbert and R.P. Agarwal, Sur la fonction de Mittag-Leffler et quelques-unes de ses généralisations, Bull. Sci. Math. II Sér 77 (1953), pp. 180–185.
- A.M. Mathai and H.J. Haubold, Mittag-Leffler Functions and Fractional Calculus, Special functions for applied scientists, Chap. 2, 2008, pp. 79–134.
- G. Mittag-Leffler, Sur la représentation analytique d'une branche uniforme d'une fonction monogène: première note, Acta Math. 23 (1900), pp. 43–62. Available at http://projecteuclid.org/euclid.acta/1485882068.
- G. Mittag-Leffler, Sur la représentation analytique d'une branche uniforme d'une fonction monogène: seconde note, Acta Math. 24 (1901), pp. 183–204. Available at http://projecteuclid.org/euclid.acta/1485882092.
- G. Mittag-Leffler, Sur la représentation analytique d'une branche uniforme d'une fonction monogène: Troisième note, Acta Math. 24 (1901), pp. 205–244. Available at http://projecteuclid.org/euclid.acta/1485882093.
- G. Mittag-Leffler, Sur la représentation analytique d'une branche uniforme d'une fonction monogène: quatrième note, Acta Math. 26 (1902), pp. 353–391. Available at http://projecteuclid.org/euclid.acta/1485882143.
- G. Mittag-Leffler, Sur la représentation analytique d'une branche uniforme d'une fonction monogène: cinquième note, Acta Math. 29 (1905), pp. 101–181. Available at http://projecteuclid.org/euclid.acta/1485887138.
- G. Mittag-Leffler, Sur la répresentation analytique d'une branche uniforme d'une fonction monogène: Sixième note, Acta Math. 42 (1920), pp. 285–308. Available at http://projecteuclid.org/euclid.acta/1485887523.
- R.I. Parovik, Calculation specific functions of Mittag-Leffler in the computer mathematics “Maple”, Bullet. KRASEC Phys. & Math. Sci. 2(5) (2012), pp. 51–61. Available at http://krasec.ru/Parovik-2-5-2012/.
- I. Podlubny, Mittag-Leffler function, 2012. Available at https://www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function.
- M. Popolizio and R. Garrappa, Fast evaluation of the Mittag-Leffler function on the imaginary axis, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014; Jun, IEEE, 2014. pp. 1–6. Available at http://ieeexplore.ieee.org/document/6967420/.
- A.Y. Popov and A.M. Sedletskii, Distribution of roots of Mittag-Leffler functions, J. Math. Sci. (United States) 190(2) (2013), pp. 209–409.
- S. Rogosin, The role of the Mittag-Leffler function in fractional modeling, Mathematics 3(2) (2015), pp. 368–381.
- V.V. Saenko, An integral representation of the Mittag-Leffler function, arXiv. 2020 Jan. Availalbe at http://arxiv.org/abs/2001.09606.
- V.V. Saenko, Singular points of the integral representation of the Mittag-Leffler function, arXiv. 2020, pp. 1–11. Available at http://arxiv.org/abs/2004.08164.
- V.V. Saenko, Two forms of the integral representations of the Mittag-Leffler function, Mathematics 8(7) (2020 jul), pp. 1101. Available at http://arxiv.org/abs/2005.11745 Available at https://www.mdpi.com/2227-7390/8/7/1101.
- H.J. Seybold and R. Hilfer, Numerical results for the generalized Mittag-Leffler function, Fract. Calc. Appl. Anal. 8(2) (2005), pp. 129–139.
- H. Seybold and R. Hilfer, Numerical algorithm for calculating the generalized Mittag-Leffler function, SIAM. J. Numer. Anal. 47(1) (2009 jan), pp. 69–88. Available at http://epubs.siam.org/doi/https://doi.org/10.1137/070700280.
- Special Functions of the Fractional Calculus, in Fractional differential equations, Podlubny I, ed., Elsevier, Mathematics in Science and Engineering; Vol. 198, Chap. 1, 1999. pp. 1–39. Availalbe at http://www.sciencedirect.com/science/article/pii/S0076539299800204.
- D.L. Suthar, H. Amsalu, and K. Godifey, Certain integrals involving multivariate Mittag-Leffler function, J. Inequal. Appl. 2019(1) (2019), pp. 2031. Available at https://doi.org/http://doi.org/10.1186/s13660-019-2162-z.
- D.L. Suthar, M. Andualem, and B. Debalkie, A study on generalized multivariable mittag-Leffler function via generalized fractional calculus operators, J. Math. 2019(4) (2019), pp. 1–7.
- V.V. Uchaikin, D.O. Cahoy, and R.T. Sibatov, Fractional processes: from poisson to branching one, Int. J. Bifur. Chaos 18(09) (2008 sep), pp. 2717–2725. Available at http://www.worldscientific.com/doi/abs/https://doi.org/10.1142/S0218127408021932.
- V.V. Uchaikin, R.T. Sibatov, and D.V. Uchaikin, Memory regeneration phenomenon in dielectrics: the fractional derivative approach, Physica Scripta 136 (2009 oct), pp. 014002. Available at https://iopscience.iop.org/article/https://doi.org/10.1088/0031-8949/2009/T136/014002.
- A. Wiman, Über den fundamentalsatz in der teorie der funktionen ea(x), Acta Mathematica 29(1) (1905), pp. 191–201.
- A. Wiman, Über die nullstellen der funktionen ea(x), Acta Mathematica 29 (1905), pp. 217–234. Available at http://projecteuclid.org/euclid.acta/1485887142.
- X. Yu, Y. Zhang, H.G. Sun, and C. Zheng, Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: analytical solution in bounded-domain and model comparison, Chaos Solitons Fractals 115 (2018), pp. 306–312. Available at https://doi.org/https://doi.org/10.1016/j.chaos.2018.08.026.