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A fast algorithm for fractional Helmholtz equation with application to electromagnetic waves propagation

Author

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  • Belevtsov, Nikita S.
  • Lukashchuk, Stanislav Yu.

Abstract

A fractional Helmholtz equation with the fractional Laplacian is investigated. Fundamental solutions of this equation and their factorized representations in terms of H-functions are constructed using Fourier and Mellin integral transforms. Multipole expansion for integral representation of the fractional Helmholtz equation’s solution is derived. A technique for evaluating H-functions from the multipole expansion is proposed. A modification of the multipole method for solving considered equation is developed. Numerical results demonstrating high efficiency of the proposed approach are presented. A fractional generalization of the mathematical model for a plane polarized electromagnetic wave propagation in the inhomogeneous medium, leading to a fractional Helmholtz equation with the fractional Laplacian, is derived and investigated using the proposed algorithm.

Suggested Citation

  • Belevtsov, Nikita S. & Lukashchuk, Stanislav Yu., 2022. "A fast algorithm for fractional Helmholtz equation with application to electromagnetic waves propagation," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    • Handle: RePEc:eee:apmaco:v:416:y:2022:i:c:s0096300321008109
    DOI: 10.1016/j.amc.2021.126728
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