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The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus.
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1930
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1953
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S. Havriliak, S. Negami, On the equivalence of dielectric and mechanical dispersions in poly( n n -hexyl methacrylate). J. Phys. D Appl. Phys. 2
1969
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S. Havriliak, S. Negami, On the equivalence of dielectric and mechanical dispersions in some polymers; e.g. poly( n n -octyl methacrylate). Polymer 10
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T. R. Prabhakar, A singular integral equation with a generalized Mittag–Leffler function in the kernel. Yokohama Math. J. 19
1971
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K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations . A Wiley-Intersci. Publ., John Wiley & Sons, Inc., New York (1993)
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S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications . Gordon and Breach Sci. Publ., Switzerland (1993)
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S. Havriliak Jr, S. J. Havriliak, Results from an unbiased analysis of nearly 1000 sets of relaxation data. J. Non-Cryst. Solids 172–174, Part 1
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R. Hilfer, L. Anton, Fractional master equation and fractal time random walks. Phys. Rev. E 51
1995
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R. Nigmatullin, Y. Ryabov, Cole–Davidson dielectric relaxation as a self-similar relaxation process. Phys. Solid State 39
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A. K. Jonscher, Dielectric relaxation in solids. J. Phys. D 32
1999
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V. Kiryakova, Multiindex Mittag-Leffler functions, related Gelfond-Leontiev operators and Laplace type integral transforms. Fract. Calc. Appl. Anal. 2
1999
Cited alongside, same era.
Yu. Luchko, Operational method in fractional calculus. Fract. Calc. Appl. Anal. 2
1999
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I. Podlubny, Fractional Differential Equations . Vol. 198 of Mathematics in Science and Engineering. Academic Press Inc., San Diego, CA (1999)
1999
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V.S. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus. J. Comput. Appl. Math. 118
2000
Cited alongside, same era.
F. Mainardi, R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math. 118
2000
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D. O. Cahoy, F. Polito, Renewal processes based on generalized Mittag-Leffler waiting times. Commun. Nonlin. Sci. Numer. Simul. 18
2013
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M. D’Ovidio, F. Polito, Fractional diffusion–telegraph equations and their associated stochastic solutions. Theory Probab. Appl. 62
2013
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R. Garrappa, M. Popolizio, Evaluation of generalized Mittag–Leffler functions on the real line. Adv. Comput. Math. 39
2013
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J. Paneva-Konovska, On the multi-index ( 3 m 3m -parametric) Mittag-Leffler functions, fractional calculus relations and series convergence. Open Phys. ( Centr. Eur. J. Phys. ) 11
2013
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R. Garra, R. Gorenflo, F. Polito, Ž. Tomovski, Hilfer-Prabhakar derivatives and some applications. Appl. Math. Comput. 242
2014
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O. N. Repin, A. I. Saichev, Fractional Poisson law. Radiophys. Quantum Electron. 43
2000
Cited alongside, same era.
A. A. Kilbas, J. J. Trujillo, Differential equations of fractional order: methods, results and problems, I. Appl. Anal. 78
2001
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R. Gorenflo, J. Loutchko, Y. Luchko, Computation of the Mittag-Leffler function E α , β ( z ) E_{\alpha,\beta}(z) and its derivative. Fract. Calc. Appl. Anal. 5
2002
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R. Hilfer, Experimental evidence for fractional time evolution in glass forming materials. Chem. Phys. 284
2002
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R. Hilfer, H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems. Phys. Rev. E 65
2002
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A. A. Kilbas, M. Saigo, R. K. Saxena, Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the kernels. J. Integral Equations Appl. 14
2002
Cited alongside, same era.
A. M. Krägeloh, Two families of functions related to the fractional powers of generators of strongly continuous contraction semigroups. J. Math. Anal. Appl. 283
2003
Cited alongside, same era.
R. Garrappa, The Mittag–Leffler function. MATLAB Central File Exchange (2014), File ID: 48154
2014
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R. Gorenflo, A. A. Kilbas, F. Mainardi, S. Rogosin, Mittag-Leffler functions. Theory and Applications . Springer Monographs in Mathematics, Springer, Berlin (2014)
2014
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J. Paneva-Konovska, Convergence of series in three parametric Mittag-Leffler functions. Math. Slovaca 64
2014
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S. Rogosin, F. Mainardi, George William Scott Blair – The pioneer of factional calculus in rheology. Commun. Appl. Ind. Math. 6
2014
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T. Sandev, Ž. Tomovski, Langevin equation for a free particle driven by power law type of noises. Phys. Lett. A 378
2014
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Ž. Tomovski, T. Pogány, H. M. Srivastava, Laplace type integral expressions for a certain three-parameter family of generalized Mittag-Leffler functions with applications involving complete monotonicity. J. Franklin Inst. 351
2014
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P. Bia, D. Caratelli, L. Mescia, R. Cicchetti, G. Maione, F. Prudenzano, A novel FDTD formulation based on fractional derivatives for dispersive Havriliak–Negami media. Signal Process. 107
2015
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R. Garrappa, Numerical evaluation of two and three parameter Mittag-Leffler functions. SIAM J. Numer. Anal. 53
2015
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F. Mainardi, R. Garrappa, On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. J. Comput. Phys. 293
2015
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T. Sandev, A. Chechkin, H. Kantz, R. Metzler, Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Fract. Calc. Appl. Anal. 18
2015
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T. Sandev, A. Chechkin, N. Korabel, H. Kantz, I. Sokolov, R. Metzler, Distributed-order diffusion equations and multifractality: models and solutions. Phys. Rev. E 92
2015
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R. Garrappa, Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models. Commun. Nonlin. Sci. Numer. Simul. 38
2016
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R. Garrappa, F. Mainardi, G. Maione, Models of dielectric relaxation based on completely monotone functions. Fract. Calc. Appl. Anal. 19
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A. Giusti, F. Mainardi, A dynamic viscoelastic analogy for fluid-filled elastic tubes. Meccanica 51
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T. K. Pogány, Z. Tomovski, Probability distribution built by Prabhakar function. Related Turán and Laguerre inequalities. Integr. Transf. Spec. Funct. 27
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F. Polito, Ž. Tomovski, Some properties of Prabhakar-type fractional calculus operators. Fract. Differ. Calc. 6
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I. Colombaro, A. Giusti, S. Vitali, Storage and dissipation of energy in Prabhakar viscoelasticity. Mathematics 6
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R. Garra, R. Garrappa, The Prabhakar or three parameter Mittag-Leffler function: Theory and application. Commun. Nonlin. Sci. Numer. Simul. 56
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R. Garrappa, M. Popolizio, Computing the matrix Mittag–Leffler function with applications to fractional calculus. J. Sci. Comput. 77
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A. Giusti, I. Colombaro, Prabhakar-like fractional viscoelasticity. Commun. Nonlin. Sci. Numer. Simul. 56
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K. Górska, A. Horzela, T. K. Lattanzi, A. Pogány, On the complete monotonicity of the three parameter generalized Mittag-Leffler function e α , β γ ( − x ) e_{\alpha,\beta}^{\gamma}(-x) . Available as arXiv: 1811.10441 (2018)
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