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Fractional calculus operators of special functions? The result is well predictable!

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  • Kiryakova, Virginia

Abstract

Recently many authors are spending lot of time and efforts to evaluate various operators of fractional order integration and differentiation and their generalizations of classes of, or particular, special functions. The list of such works is rather long and yet growing daily, so we limit ourselves to mention here only a few, just to illustrate our general approach. As special functions present indeed a great variety, and the operators of fractional calculus do as well, the mentioned job produces a huge flood of publications. Many of them use same formal and standard procedures, and besides, often the results sound not of practical use, with except to increase authors’ publication activities.

Suggested Citation

  • Kiryakova, Virginia, 2017. "Fractional calculus operators of special functions? The result is well predictable!," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 2-15.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:2-15
    DOI: 10.1016/j.chaos.2017.03.006
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    References listed on IDEAS

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    1. K. S. Nisar & S. R. Mondal & P. Agarwal, 2016. "Composition Formulas of Bessel-Struve Kernel Function," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-8, May.
    2. Saiful R. Mondal & K. S. Nisar, 2014. "Marichev-Saigo-Maeda Fractional Integration Operators Involving Generalized Bessel Functions," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, April.
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    Cited by:

    1. Khan, Tahir Ullah & Khan, Muhammad Adil, 2021. "New generalized mean square stochastic fractional operators with applications," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Virginia Kiryakova, 2020. "Unified Approach to Fractional Calculus Images of Special Functions—A Survey," Mathematics, MDPI, vol. 8(12), pages 1-35, December.
    3. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
    4. Jordanka Paneva-Konovska, 2022. "Taylor Series for the Mittag–Leffler Functions and Their Multi-Index Analogues," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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    2. Virginia Kiryakova, 2020. "Unified Approach to Fractional Calculus Images of Special Functions—A Survey," Mathematics, MDPI, vol. 8(12), pages 1-35, December.

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