A prelude to the fractional calculus applied to tumor dynamic

A prelude to the fractional calculus applied to tumor dynamic

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 1, in one v...

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Main Authors: N. Varalta, A.V. Gomes, R.F. Camargo
Format: Article
Language:English
Published: Sociedade Brasileira de Matemática Aplicada e Computacional
Series:TEMA
Subjects:
biomathematics
fractional calculus
logistics equation
dynamics of cancer tumor
Online Access:http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000200008&lng=en&tlng=en
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spelling doaj-578e7d861caf4b1ab84f5a1df9a90f4c2020-11-25T03:56:26ZengSociedade Brasileira de Matemática Aplicada e ComputacionalTEMA2179-845115221122110.5540/tema.2014.015.02.0211S2179-84512014000200008A prelude to the fractional calculus applied to tumor dynamicN. Varalta0A.V. Gomes1R.F. Camargo2Universidade Estadual PaulistaUniversidade Estadual PaulistaUniversidade Estadual PaulistaIn 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 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000200008&lng=en&tlng=enbiomathematicsfractional calculuslogistics equationdynamics of cancer tumor
collection DOAJ
language English
format Article
sources DOAJ
author N. Varalta
A.V. Gomes
R.F. Camargo
spellingShingle N. Varalta
A.V. Gomes
R.F. Camargo
A prelude to the fractional calculus applied to tumor dynamic
TEMA
biomathematics
fractional calculus
logistics equation
dynamics of cancer tumor
author_facet N. Varalta
A.V. Gomes
R.F. Camargo
author_sort N. Varalta
title A prelude to the fractional calculus applied to tumor dynamic
title_short A prelude to the fractional calculus applied to tumor dynamic
title_full A prelude to the fractional calculus applied to tumor dynamic
title_fullStr A prelude to the fractional calculus applied to tumor dynamic
title_full_unstemmed A prelude to the fractional calculus applied to tumor dynamic
title_sort prelude to the fractional calculus applied to tumor dynamic
publisher Sociedade Brasileira de Matemática Aplicada e Computacional
series TEMA
issn 2179-8451
description 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 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 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.
topic biomathematics
fractional calculus
logistics equation
dynamics of cancer tumor
url http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000200008&lng=en&tlng=en
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