Classes of operators in fractional calculus: A case study

[1]  D. Baleanu,et al.  On Fractional Operators and Their Classifications , 2019, Mathematics.

[2]  Neville J. Ford,et al.  Comparison of numerical methods for fractional differential equations , 2006 .

[3]  Andrea Giusti General fractional calculus and Prabhakar's theory , 2020, Commun. Nonlinear Sci. Numer. Simul..

[4]  Clara-Mihaela Ionescu,et al.  The role of fractional calculus in modeling biological phenomena: A review , 2017, Commun. Nonlinear Sci. Numer. Simul..

[5]  T. R. Prabhakar A SINGULAR INTEGRAL EQUATION WITH A GENERALIZED MITTAG LEFFLER FUNCTION IN THE KERNEL , 1971 .

[6]  S. Kalla,et al.  Multivariate analogue of generalized Mittag-Leffler function , 2011 .

[7]  A. Atangana,et al.  New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model , 2016, 1602.03408.

[8]  Arran Fernandez,et al.  A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators , 2020, Comput. Appl. Math..

[9]  Dumitru Baleanu,et al.  Relaxation and diffusion models with non-singular kernels , 2017 .

[10]  D. Baleanu,et al.  Relations between fractional models with three-parameter Mittag-Leffler kernels , 2020 .

[11]  Dumitru Baleanu,et al.  On fractional calculus with general analytic kernels , 2019, Appl. Math. Comput..

[12]  R. K. Saxena,et al.  Generalized mittag-leffler function and generalized fractional calculus operators , 2004 .

[13]  On a new definition of fractional differintegrals with Mittag-Leffer kernel , 2018, Filomat.

[14]  M. Ali Özarslan,et al.  Bivariate Mittag-Leffler functions arising in the solutions of convolution integral equation with 2D-Laguerre-Konhauser polynomials in the kernel , 2019, Appl. Math. Comput..

[15]  YangQuan Chen,et al.  A new collection of real world applications of fractional calculus in science and engineering , 2018, Commun. Nonlinear Sci. Numer. Simul..

[16]  Tadeusz Kaczorek,et al.  Positive linear systems with different fractional orders , 2010 .

[17]  Federico Polito,et al.  A practical guide to Prabhakar fractional calculus , 2020, Fractional Calculus and Applied Analysis.

[18]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[19]  B. Ross,et al.  Fractional Calculus and Its Applications , 1975 .

[20]  Igor Podlubny,et al.  Shadows on the walls: Geometric interpretation of fractional integration , 2007 .

[21]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[22]  Yuri Luchko Fractional derivatives and the fundamental theorem of fractional calculus , 2020, 2006.14383.

[23]  Dumitru Baleanu,et al.  On some new properties of fractional derivatives with Mittag-Leffler kernel , 2017, Commun. Nonlinear Sci. Numer. Simul..

[24]  J. Sabatier Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive? , 2020, Fractal and Fractional.

[25]  Changpin Li,et al.  Numerical methods for fractional partial differential equations , 2018, Int. J. Comput. Math..

[26]  Federico Polito,et al.  Hilfer-Prabhakar derivatives and some applications , 2014, Appl. Math. Comput..

[27]  Yuri Luchko,et al.  Desiderata for Fractional Derivatives and Integrals , 2019, Mathematics.

[28]  Dumitru Baleanu,et al.  Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions , 2018, Commun. Nonlinear Sci. Numer. Simul..

[29]  C. Cattani,et al.  A new general fractional-order derivataive with Rabotnov fractional-exponential kernel applied to model the anomalous heat transfer , 2019, Thermal Science.

[30]  Thomas J. Osler,et al.  Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series , 1970 .

[31]  R. Herrmann,et al.  Fractional Calculus: an Introduction for Physicists (2nd Edition) , 2014 .

[32]  T. Hartley,et al.  Initialization of Fractional-Order Operators and Fractional Differential Equations , 2008 .

[33]  Jordan Hristov,et al.  Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative , 2016 .

[34]  Baleanu Dumitru Comments on: “The failure of certain fractional calculus operators in two physical models” by M. Ortigueira, V. Martynyuk, M. Fedula and J.A.T. Machado , 2020 .