The Time–Fractional Wave Equation with Variable Coefficients

Chenkuan Li ()
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Chenkuan Li: Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada

Mathematics, 2025, vol. 13, issue 15, 1-18

Abstract: In this paper, we primarily use the inverse operator method to find a unique series solution to a time–fractional wave equation with variable coefficients based on the Mittag–Leffler function. In addition, we also derive the series and integral convolution solutions to the Klein–Gordon equation using the Fourier transform and Green’s functions. Furthermore, our series solutions significantly simplify the process of finding solutions with several illustrative examples, avoiding the need for complicated integral computations.

Keywords: Mittag–Leffler function; time–fractional wave equation; inverse operator method; Fourier transform; time–fractional Klein–Gordon equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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