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Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus

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Abstract

This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [3, 4] or Addendum to [22]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for functions meromorphic in the unit disc of the complex plane [11]. The contemporary development of M.M. Djrbashian’s ideas can be found in the recent monograph [22]. The survey intends to complete the survey article “Mkhitar Djrbashian and his contribution to fractional calculus" [25], which described the contribution of M.M. Djrbashian mainly from the point of view of basic constructions of the fractional calculus, to the theory of fractional differential equations and integral transforms.

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Acknowledgements

Joel E. Restrepo was supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and the Methusalem program of the Ghent University Special Research Fund (BOF) (Grant number 01M01021).

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Armenia, 24/5 Marshal Baghramian Ave., 0019, Yerevan, Republic of Armenia

    Armen M. Jerbashian

  2. Department of Mathematics, Yerevan State University, 1 Alex Manoogian, 0025, Yerevan, Republic of Armenia

    Spartak G. Rafayelyan

  3. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, 9000, Ghent, Belgium

    Joel E. Restrepo

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  1. Armen M. Jerbashian
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  2. Spartak G. Rafayelyan
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  3. Joel E. Restrepo
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Jerbashian, A.M., Rafayelyan, S.G. & Restrepo, J.E. Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus. Fract Calc Appl Anal (2024). https://doi.org/10.1007/s13540-024-00267-3

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