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Granular Computing
Published in: Granular Computing 6/2023

20-07-2023 | Original Paper

Solution of the Pythagorean fuzzy wave equation with Pythagorean fuzzy Fourier sine transform

Authors: Muhammad Akram, Muhammad Yousuf, Tofigh Allahviranloo

Published in: Granular Computing | Issue 6/2023

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Abstract

The 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.
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Metadata
Title
Solution of the Pythagorean fuzzy wave equation with Pythagorean fuzzy Fourier sine transform
Authors
Muhammad Akram
Muhammad Yousuf
Tofigh Allahviranloo
Publication date
20-07-2023
Publisher
Springer International Publishing
Published in
Granular Computing / Issue 6/2023
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-023-00400-2

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