Akram, MuhammadYousuf, MuhammadAllahviranloo, Tofigh2024-05-192024-05-1920232364-49662364-4974https://doi.org10.1007/s41066-023-00400-2https://hdl.handle.net/20.500.12713/5165The main objective of this research article is to study the analytical solution of the Pythagorean fuzzy wave equation under the generalized Hukuhara partial differentiability using the Pythagorean fuzzy Fourier sine transform. Some concepts of multivariate Pythagorean fuzzy-valued functions and their gH-partial differentiability along with integrability are given. The notions of Pythagorean fuzzy Fourier sine transform and Pythagorean fuzzy Fourier inverse sine transform are introduced along with some fundamental properties. Furthermore, a new Pythagorean fuzzy wave equation model is developed under gH-differentiability using the Pythagorean fuzzy Fourier sine transform. Some numerical examples are solved with the proposed method and their solutions are displayed graphically to verify and support theoretical results. A practical application of the Pythagorean fuzzy wave equation to magnetic resonance imaging is also described.eninfo:eu-repo/semantics/closedAccessGeneralized Hukuhara-Partial DifferentiabilityPythagorean Fuzzy Multivariate FunctionWave EquationMultivariate Fourier Sine TransformReview Article8611491171WOS:0010327450000012-s2.0-85165238906N/A10.1007/s41066-023-00400-2Q1