Yazar "Yousuf, Muhammad" seçeneğine göre listele

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    An analytical study of Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy fourier transform under generalized Hukuhara Caputo fractional differentiability
    (Springernature, 2024) Akram, Muhammad; Yousuf, Muhammad; Allahviranloo, Tofigh
    Pythagorean fuzzy fractional calculus provides a strong framework for modeling and analyzing complicated systems with uncertainty and indeterminacy. The primary focus of this article is to investigate the analytical solution of the Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy Fourier transform under generalized Hukuhara Caputo fractional differentiability. To this end, we first establish generalized Hukuhara Caputo fractional differentiability in the context of multivariate Pythagorean fuzzy-valued functions and then we present some results of multivariate Pythagorean generalized Hukuhara Caputo fractional differentiability and generalized Hukuhara integrability. We present the concept of multivariate Pythagorean fuzzy Fourier transform and give some results for Pythagorean fuzzy Fourier transforms of second-order generalized Hukuhara partial differentiability. Finally, we provide a practical application of the Pythagorean fuzzy fractional wave equation to visco-elastic materials including polymers and biological tissues. Their graphs are analyzed to visualize and support the theoretical findings.
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    Solution of the Pythagorean fuzzy wave equation with Pythagorean fuzzy Fourier sine transform
    (Springernature, 2023) Akram, Muhammad; Yousuf, Muhammad; Allahviranloo, Tofigh
    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.