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Solving Pythagorean fuzzy partial fractional diffusion model using the Laplace and Fourier transforms.

Muhammad Akram1, Tayyaba Ihsan1

  • 1Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.

Granular Computing
|April 16, 2024
PubMed
Summary

This study introduces a novel mathematical model to track COVID-19 vaccine diffusion in humans. The Pythagorean fuzzy partial fractional differential equation provides an accessible method for analyzing vaccine effects.

Keywords:
COVID-19 vaccinationCaputo generalized Hukuhara partial differentiabilityPartial fractional differential equationPythagorean fuzzy integral transforms

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Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Biomedical Engineering

Background:

  • Mathematical models for COVID-19 often require advanced mathematical expertise.
  • A simplified approach is needed to understand COVID-19 vaccine diffusion in humans.

Purpose of the Study:

  • To develop and analyze a mathematical model for COVID-19 vaccine diffusion in the human body.
  • To utilize Pythagorean fuzzy integral transforms for modeling vaccination effects.

Main Methods:

  • Established a Pythagorean fuzzy partial fractional differential equation.
  • Employed Pythagorean fuzzy Laplace and Fourier transforms for analytical solutions.
  • Applied generalized Hukuhara partial differential conditions.

Main Results:

  • Extracted analytical solutions for the vaccine diffusion model.
  • Presented key postulates and results for the applied fuzzy transforms.
  • Visualized and analyzed model behavior to support the proposed approach.

Conclusions:

  • The developed Pythagorean fuzzy model offers an efficient method for analyzing COVID-19 vaccine diffusion.
  • This approach has significant potential for bio-mathematical modeling in science and medicine.