A Caputo fractional derivative of a function with respect to another function
Data(s) |
06/10/2016
01/03/2017
|
---|---|
Resumo |
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided. |
Identificador |
1007-5704 |
Idioma(s) |
eng |
Publicador |
Elsevier |
Relação |
FCT - UID/MAT/04106/2013 http://dx.doi.org/10.1016/j.cnsns.2016.09.006 |
Direitos |
restrictedAccess |
Palavras-Chave | #Fractional calculus #Semigroup law #Numerical methods #Population growth model |
Tipo |
article |