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Generalized time-fractional telegrapher’s equation in transmission line modeling

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Abstract

An original generalization of telegrapher’s equation is derived by considering the topological generalization of the elementary circuit used in transmission line modeling in order to include the effects of charge accumulation along the line. Also, capacitive and inductive phenomena are assumed to display hereditary effects modeled by the use of fractional calculus. Although developed primarily for transmission lines, the proposed model can be applied to a wider class of diffusion-wave phenomena. The Laplace transform technique is used in obtaining the analytical solution of signal propagation along the line. Several examples illustrate good agreement between results obtained by means of the proposed analytical procedure and numerical techniques for inversion of the Laplace transform.

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Acknowledgements

This work was partially supported by Serbian Ministry of Science, Education and Technological Development, under Grants III42004 (SC), 174005 (DZ), and TR32018, TR33013 (MRR), as well as by Provincial Government of Vojvodina under Grant 114-451-2098.

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Authors and Affiliations

  1. Department of Power, Electronic and Telecommunication Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21000, Serbia

    Stevan M. Cvetićanin

  2. Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, Belgrade, 11000, Serbia

    Dušan Zorica

  3. Department of Physics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 3, Novi Sad, 21000, Serbia

    Dušan Zorica

  4. Department of Computing and Control Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića, 6, Novi Sad, 21000, Serbia

    Milan R. Rapaić

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  1. Stevan M. Cvetićanin
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  2. Dušan Zorica
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Correspondence to Milan R. Rapaić.

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Cvetićanin, S.M., Zorica, D. & Rapaić, M.R. Generalized time-fractional telegrapher’s equation in transmission line modeling. Nonlinear Dyn 88, 1453–1472 (2017). https://doi.org/10.1007/s11071-016-3322-z

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  • DOI: https://doi.org/10.1007/s11071-016-3322-z

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