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A Prelude to the Fractional Calculus Applied to Tumor Dynamic

2014; Sociedade Brasileira de Matemática Aplicada e Computacional; Volume: 15; Issue: 2 Linguagem: Inglês

10.5540/tema.2014.015.02.0211

2179-8451

Rubens de Figueiredo Camargo, Arianne Vellasco Gomes, Najla Varalta,

Gene Regulatory Network Analysis

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i. e., we replace the ordinary derivative of order one in the usual equation by a non-integer derivative of order $ 0 < \alpha \leq 1$, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.