Fractal modeling of non-integer Newtonian fluid through comparison of Sumudu and Laplace transforms

The exploration for knowing the complexity of fractal patterns (Koch snowflake, Julia shape, Chaos pro, Sierpinski triangle and Mandelbrot shape) among the rheological fluid models enables self-similar structures at different scales. In this paper, a fractal–fractional modeling of Newtonian fluid flow is developed for the velocity field by invoking power law kernel. In order to envisage the distinct computational characteristics and applications, the comparative analysis for the Sumudu transform and Laplace transform is investigated for fractal–fractional model of Newtonian fluid under exact analytical solutions. By employing fractal versus non-fractal parameters, analytical solutions for fractal–fractional model of Newtonian fluid by means of fractal Sumudu transform and fractal Laplace transform have been deduced by substituting [Formula: see text]. The sensitivity analysis for fractal–fractional model of Newtonian fluid is also emphasized for the sake of rheological phenomenon via multiple regression, Pearson correlation and probable error. Our results suggest that variations of viscosity depicted the behavior of shear stress on Newtonian fluid and predicted the complex motion under resistance of Newtonian fluid.