Filipin III br Substituting the parameters described in into
Substituting the parameters described in (56) into the model
The numerical results given in Fig. 4a–d shows numerical simu-lations of the special solution of our model as function of time for different values of αn for n ∈ [1; 5].
The solution of the model (57) can be obtained applying the
Adams-Bashforth method . The Numerical scheme is given by In this paper, we study a fractional breast cancer model. The
mathematical model is built using a Liouville–Caputo and Caputo–
Fabrizio–Caputo fractional derivatives. We consider the integer or-
der malaria transmission model proposed in  and modify it Filipin III to
become a fractional order model. Special solutions using an iter-
ative scheme via Laplace transform were obtained and the fixed
point theorem is discussed to prove the existence and uniqueness
of the coupled-solutions. Furthermore, we obtain numerical solu-
tions considering the Atangana–Toufik numerical scheme. We can
observe that the results obtained by using the Caputo–Fabrizio–
Caputo fractional derivative are different to those obtained by the
derivative of Liouville–Caputo type, for the first fractional deriva-
tive the memory effect is more evident. The numerical solutions
showed that the dynamical behaviour of the breast cancer model
depends on the fractional derivative. Also new behaviors have been
Declaration of Competing Interest
Jesús Emmanuel Solís Pérez acknowledges the support pro-
KTn−1 (tn−1 )En−1 (tn−1 ) , vided by CONACyT through the assignment doctoral fellowship.
by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014
and the support provided by SNI-CONACyT.
n F n
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