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Analysis reveals closed-form solutions for a fractional wave equation in fractional-dimensional space, indicating substantial potential applications.
This study presents an analytical solution to the fractional wave equation incorporating the Riesz fractional derivative (RFD) of the form (− Δ ) γ /2 , where 0 < γ ≤ 2 is the order of RFD. The equation is formulated within a fractional‐dimensional spatial domain, with the dimension d constrained to the interval 2 < d ≤ 3. The solution methodology is based on the fractional Fourier transform technique (FFTT) developed by Muslih and Agrawal. Solutions are derived in closed form using Fox H ‐functions (FHFs), represented through their Mellin–Barnes integral formulations. The analysis confirms the existence of valid solutions for all admissible values of γ in the range (0, 2].
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Sami I. Muslih (2025) studied this question.
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