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Generalized fractional Dirac type operators

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Abstract

We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.

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Acknowledgements

First and third authors were supported by the Nazarbayev University Program 20122022CRP1601. The first and second authors were supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). MR is also supported by EPSRC grant EP/R003025/2 and FWO Senior Research Grant G011522N. This research is funded by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant number BR21882172).

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Authors and Affiliations

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

    Joel E. Restrepo & Michael Ruzhansky

  2. School of Mathematical Sciences, Queen Mary University of London, London, England, UK

    Michael Ruzhansky

  3. Department of Mathematics, Nazarbayev University, Astana, Kazakhstan

    Durvudkhan Suragan

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  1. Joel E. Restrepo
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Restrepo, J.E., Ruzhansky, M. & Suragan, D. Generalized fractional Dirac type operators. Fract Calc Appl Anal 26, 2720–2756 (2023). https://doi.org/10.1007/s13540-023-00209-5

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