Abstract
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.
Highlights
The art of getting a differential equation whose solution describes well the reality, brings a great difficulty, generally the closer we are to perfectly describe a real problem the harder and complex the equations involved are, in Albert Einstein words [2]“One thing I have learned in a long life: all our science, measured against reality, is primitive and childlike – and yet it is the most precious thing we have”.In this sense, the so-called Fractional Calculus, which is the branch of mathematics that deals with the study of integrals and derivatives of non-integer orders, plays an outstanding role
The purpose of this paper is to present the analytic solution of the fractional logistic equation, in the inverse form, and analyze the applicability of this fractional equation to improve the description of the dynamic of cancer tumor and compare this model with some classical models presented in the literature [9, 18], and is organized as follows
The Fractional Calculus is nearly as old as the entire order one, but just in end of last century this valuable tool became evident, especially in modeling phenomena that possess time dependence, since fractional derivatives excellently describe memory effects when encountered derived from their entire order
Summary
The art of getting a differential equation whose solution describes well the reality, brings a great difficulty, generally the closer we are to perfectly describe a real problem the harder and complex the equations involved are, in Albert Einstein words [2]“One thing I have learned in a long life: all our science, measured against reality, is primitive and childlike – and yet it is the most precious thing we have” In this sense, the so-called Fractional Calculus, which is the branch of mathematics that deals with the study of integrals and derivatives of non-integer orders, plays an outstanding role.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
