Geodesic
Inverse Problem for Finding the Order of the Fractional Derivative in the Wave Equation
Matematičeskie zametki, Tome 110 (2021) no. 6, pp. 824-836

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The paper investigates an inverse problem for finding the order of the fractional derivative in the sense of Gerasimov–Caputo in the wave equation with an arbitrary positive self-adjoint operator $A$ having a discrete spectrum. By means of the classical Fourier method, it is proved that the value of the projection of the solution onto some eigenfunction at a fixed time uniquely restores the order of the derivative. Several examples of the operator $A$ are discussed, including a linear system of fractional differential equations, fractional Sturm–Liouville operators, and many others.
Keywords: wave equation, fractional derivative in the sense of Gerasimov–Caputo, inverse problems for determining the order of the derivative. 
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     author = {R. R. Ashurov and Yu. \`E. Fayziev},
     title = {Inverse {Problem} for {Finding} the {Order} of the {Fractional} {Derivative} in the {Wave} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
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R. R. Ashurov; Yu. È. Fayziev. Inverse Problem for Finding the Order of the Fractional Derivative in the Wave Equation. Matematičeskie zametki, Tome 110 (2021) no. 6, pp. 824-836. http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a1/