Modeling tumor growth using fractal calculus: Insights into tumor dynamics.

Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)". We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer.

Electrical circuits involving fractal time.

In this paper, we develop fractal calculus by defining improper fractal integrals and their convergence and divergence conditions with related tests and by providing examples. Using fractal calculus that provides a new mathematical model, we investigate the effect of fractal time on the evolution of the physical system, for example, electrical circuits. In these physical models, we change the dimension of the fractal time; as a result, the order of the fractal derivative changes; therefore, the corresponding solutions also change.

Diffusion on Middle- Cantor Sets.

In this paper, we study Cζ-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the Cζ-calculus on the generalized Cantor sets known as middle-ξ Cantor sets.