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Photoacoustic tomography (PAT) is a novel and rapidly promising technique inthe field of medical imaging, based on the generation of acoustic waves insidean object of interest by stimulating non-ionizing laser pulses. This acousticwave is measured using the detector on the outside of the object and convertedinto an image of the human body by several inversions. Thus, one ofmathematical problems in PAT is how to recover the initial function from thesolution of the wave equation on the outside of the object. In this study weconsider the fractional wave equation and assume that the point-like detectorsare located on the sphere and hyperplane. We provide how to recover the initialfunction from the data, the solution of the fractional wave equation, measuredon the sphere and hyperplane.

Reconstruction of the initial function from the solution of the fractional wave equation measured in two geometric settings