Geodesic
Monotone iterative method for fractional differential equations
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, by using the lower and upper solution method, we prove the existence of iterative solutions for a class of fractional initial value problem with non-monotone term $$\displaylines{ D_{0+}^\alpha u(t)=f(t, u(t)), \quad t \in (0, h), \cr t^{1-\alpha}u(t)\big|_{t=0} = u_0 \neq 0, }$$ where $0$ is the standard Riemann-Liouville fractional derivative, $0\alpha 1$. A new condition on the nonlinear term is given to guarantee the equivalence between the solution of the IVP and the fixed-point of the corresponding operator. Moreover, we show the existence of maximal and minimal solutions.
Classification : 34B15, 34A08
Keywords: fractional initial value problem, lower and upper solution method, existence of solutions 
@article{EJDE_2016__2016__a57,
     author = {Bai, Zhanbing and Shuo, Zhang and Sun, Sujing and Yin, Chun},
     title = {Monotone iterative method for fractional differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a57/}
}
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Bai, Zhanbing; Shuo, Zhang; Sun, Sujing; Yin, Chun. Monotone iterative method for fractional differential equations. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a57/