Mittag-Leffler

Mittag-Leffler function: This is a MATLAB routine for evaluating the Mittag-Leffler function with two parameters (sometimes also called generalized exponential function). The Mittag-Leffler function with two parameters plays an important role and appears frequently in solutions of fractional differential equations (i.e. differential equations containing fractional derivatives).


References in zbMATH (referenced in 37 articles )

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  1. Iyiola, O.S.; Asante-Asamani, E.O.; Wade, B.A.: A real distinct poles rational approximation of generalized Mittag-Leffler functions and their inverses: applications to fractional calculus (2018)
  2. Li, Zhuo; Liu, Lu; Dehghan, Sina; Chen, Yangquan; Xue, Dingyü: A review and evaluation of numerical tools for fractional calculus and fractional order controls (2017)
  3. Rosenfeld, Joel A.; Dixon, Warren E.: Approximating the Caputo fractional derivative through the Mittag-Leffler reproducing kernel Hilbert space and the kernelized Adams-Bashforth-Moulton method (2017)
  4. Xue, Dingyü: Fractional-order control systems. Fundamentals and numerical implementations (2017)
  5. Zaman, Sharif F.; Baleanu, Dumitru; Petráš, Ivo: Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler function (2016)
  6. Aceto, Lidia; Magherini, Cecilia; Novati, Paolo: On the construction and properties of $m$-step methods for FDEs (2015)
  7. Dybiec, Bartłomiej; Sokolov, Igor M.: Estimation of the smallest eigenvalue in fractional escape problems: semi-analytics and fits (2015)
  8. Tejado, Inés; Vinagre, Blas M.; Torres, Daniel; López-Bernal, Álvaro; Villalobos, Francisco J.; Testi, Luca; Podlubny, Igor: Fractional approach for estimating sap velocity in trees (2015)
  9. Wang, Jun-Gang; Wei, Ting; Zhou, Yu-Bin: Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation (2015)
  10. Xue, Dingyü; Chen, YangQuan: Modeling, analysis and design of control systems in MATLAB and Simulink (2015)
  11. Zeng, Caibin; Chen, Yang Quan: Global Padé approximations of the generalized Mittag-Leffler function and its inverse (2015)
  12. Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.: Mittag-Leffler functions, related topics and applications (2014)
  13. Mainardi, Francesco: On some properties of the Mittag-Leffler function $E_\alpha(-t^\alpha)$, completely monotone for $t>0$ with $0<\alpha<1$ (2014)
  14. Novati, P.: Numerical approximation to the fractional derivative operator (2014)
  15. Ott, Curdin: Bottleneck options (2014)
  16. Wei, Ting; Wang, Jungang: A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation (2014)
  17. Wei, Ting; Wang, Jun-Gang: A modified quasi-boundary value method for the backward time-fractional diffusion problem (2014)
  18. Wei, Ting; Zhang, Zheng-Qiang: Stable numerical solution to a Cauchy problem for a time fractional diffusion equation (2014)
  19. Duan, Jun-Sheng; Wang, Zhong; Liu, Yu-Lu; Qiu, Xiang: Eigenvalue problems for fractional ordinary differential equations (2013)
  20. Fulger, Daniel; Scalas, Enrico; Germano, Guido: Random numbers from the tails of probability distributions using the transformation method (2013)

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