Fuzzy-fractional modeling and analysis of gas dynamics via extended He-Laplace-Carson algorithm

Abstract The primary objective of this study is to model, solve, and analyze fractional-order nonlinear gas dynamics using fuzzy logic. Triangular fuzzy numbers (TFNs) are employed to represent uncertainties in reaction and convection parameters, as well as other uncertainties inherent in the gas dynamics model. After fuzzifying the model, it is solved using He-Laplace-Carson Algorithm, which combines homotopy perturbation and Laplace-Carson transformation. The efficiency of the proposed methodology is evaluated through residual errors in the upper and lower bound solutions. Four test problems, incorporating different fuzzy parameters, are explored, and their effects are analyzed using 2D, 3D, and contour plots at the upper and lower bounds. The results indicate that uncertainty significantly impacts the gas dynamics model. This approach offers researchers and engineers a more accurate and computationally efficient means to account for uncertainties and noise in various models.