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

Many mathematical models describe the Corona virus disease 2019 (COVID-19) outbreak; however, they require advance mathematical skills. The need for this study is to determine the diffusion of the COVID-19 vaccine in humans. To this end, we first establish a Pythagorean fuzzy partial fractional differential equation using the Pythagorean fuzzy integral transforms to express the effects of COVID-19 vaccination on humans under the generalized Hukuhara partial differential conditions. We extract the analytical solution of the Pythagorean fuzzy partial fractional differential equation using the Pythagorean fuzzy Laplace transform under the generalized Hukuhara partial differential and the Pythagorean fuzzy Fourier transform using the Caputo generalized Hukuhara partial differential. Moreover, we present some essential postulates and results related to the Pythagorean fuzzy Laplace transform and the Pythagorean fuzzy Fourier transform. Furthermore, we develop the solution procedure to extract the solution of the Pythagorean fuzzy partial fractional differential equation. To grasp the considered approach, a mathematical model for the diffusion of the COVID-19 vaccination in the human body is provided and analyzed the behavior to visualize and support the proposed model. Our proposed method is efficient and has a great worth to discuss the bio-mathematical models in various fields of science and medicines.