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GENERAL FRACTIONAL CALCULUS OPERATORS CONTAINING THE GENERALIZED MITTAG-LEFFLER FUNCTIONS APPLIED TO ANOMALOUS RELAXATION

ABSTRACT
In this paper, we address a family of the general fractional calculus operators of Wiman and Prabhakar types for the first time. The general Mittag-Leffler function to structure the kernel functions of the fractional order derivative operators and their Laplace integral transforms are considered in detail. The formulations are as the mathematical tools proposed to investigate the anomalous relaxation.
KEYWORDS
PAPER SUBMITTED: 2017-03-10
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-05-20
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI170510196Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S317 - S326]
REFERENCES
  1. Gorenflo, R., et al., Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin, 2014
  2. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2005
  3. Samko, S. G., et al., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993
  4. Mittag-Leffler, G. M., Sur La Nouvelle Fonction ()Exα, Comptes Rendus de l'Acad´emie des Sciences, 137 (1903), pp. 554-558
  5. Wiman, A., Über Den Fundamental Satz in Der Theorie Der Funktionen ()Exα, Acta Mathematica, 29 (1905), pp. 217-234
  6. Prabhakar, T. R., A Singular Integral Equation with a Generalized Mittag Leffler Function in the Kernel, Yokohama Mathematical Journal, 19 (1971), 1, pp. 7-15
  7. Shukla, A. K., Prajapati, J. C., On a Generalization of Mittag-Leffler Function and Its Properties, Journal of Mathematical Analysis and Applications, 336 (2007), 2, pp. 797-811
  8. Kilbas, A. A., et al., Generalized Mittag-Leffler Function and Generalized Fractional Calculus Operators, Integral Transforms and Special Functions, 15 (2004), 1, pp. 31-49
  9. Yang, X. J., New General Fractional-order Rheological Models within Kernels of Mittag-Leffler Functions, Romanian Reports in Physics, 2017, in press
  10. Giusti, A., et al., Prabhakar-like Fractional Viscoelasticity, Communications in Nonlinear Science and Numerical Simulation, 58 (2018), 1, pp.138-143
  11. Yang, X. J., Fractional Derivatives of Constant and Variable Orders Applied to Anomalous Relaxation Models in Heat-Transfer Problems, Thermal Science, 21 (2017), 3, pp.1161-1171
  12. Atangana, A., et al., New Fractional Derivatives with Nonlocal and Non-singular Kernel: Theory and Application to Heat Transfer Model, Thermal Science, 20 (2016), 2, 763-769.
  13. Yang, X. J., et al., Anomalous Diffusion Models with General Fractional Derivatives within the Kernels of the Extended Mittag-Leffler Type Functions, Romanian Reports in Physics, 2017, in press
  14. Yang, X. J., General Fractional Derivatives: a Tutorial Comment, Symposium on Advanced Computational Methods for Linear and Nonlinear Heat and Fluid Flow 2017 & Advanced Computational Methods in Applied Science 2017& Fractional (Fractal) Calculus and Applied Analysis 2017, July 1-3, 2017, Songjiang, Shanghai, China

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence