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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
