Das transformadas integrais ao cálculo fracionário aplicado à equação logística - Varalta, Najla [UNESP] (2014)
This work presents the definitions of some important functions inherent to Fractional Calculus as well as the definitions for Fractional Integral and Fractional Derivative. One of the main goals of this work is to solve real problems, that is why focus was given on fractional derivatives, in accordance with Caputo, once this definition is more pertinent to this kind of problem. It was introduced the exponential model wich describes bacterial growth in an ideal way and it was proposed its generalization through Fractional Calculus. In order to refine the solution given by the classical logistic equation and expand its application range in the study of tumor dynamics, we propose and solve its generalization, using the Fractional Calculus , i. e., we replace the derivative of order 1 in the ordinary equation by a non-integer order derivative 0 < ≤ 1. In both cases, the solution of the fractional equation has as a special case the solution of the classic model. Finally, we present the original part of this work, i.e., we analyse the applicability of the fractional logistic model to describe the growth of cancer tumor, that is, we compare the model with some presented in the literature and showed graphically that in several cases our model is more convenient than the usual ones