Abstract
In this paper, we investigate non-homogeneous wave equations in fractional space-time domains of space dimension D, \(0 < D \le 3\) and time dimension \(\beta\), \(0 < \beta \le 1\). We write the wave equations in terms of potential functions and non-zero source terms. For scalar source terms, the potential functions are also scalar functions, and for vector source terms, the potential functions are vector functions. We derived an expression for the wave to propagate from the source point to the observation point. The study shows that the time for a wave to propagate from the source point to the observation point in a fractional space-time domain could be different from that in an integer order space-time domain.
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Acknowledgements
The author would like to sincerely thank Al-Azhar University-Gaza for providing him the financial support and the Department of Mechanical Engineering and Energy Processes (MEEP) and the Dean of Graduate Studies at Southern Illinois University, Carbondale (SIUC), IL, for providing him the necessary facilities during his stay at SIUC. Also, the author would like to sincerely thank Prof. Om P. Agrawal and the reviewers for their constructive comments.
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Muslih, S.I. Propagation of Electromagnetic Waves in Fractional Space Time Dimensions. Found Phys 53, 37 (2023). https://doi.org/10.1007/s10701-023-00677-y
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DOI: https://doi.org/10.1007/s10701-023-00677-y