Geodesic
Existence and uniqueness of mild solutions for fractional semilinear differential equations
Electronic Journal of Differential Equations, Tome 2015 (2015).

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

Summary: In this article, we study the existence and uniqueness of a local mild solution for a class of semilinear differential equations involving the Caputo fractional time derivative of order $\alpha(0\alpha1)$ and, in the linear part, a sectorial linear operator A. We put some conditions on a nonlinear term f and an initial data $u_0$ in terms of the fractional power of A. By applying Banach's Fixed Point Theorem, we obtain a unique local mild solution with smoothing effects, estimates, and a behavior at t close to 0. An example as an application of our results is also given.
Classification : 34A08, 34A12
Keywords: fractional semilinear differential equation, sectorial operator, Caputo fractional derivative, fractional power, mild solution 
@article{EJDE_2015__2015__a71,
     author = {Guswanto, Bambang Hendriya and Suzuki, Takashi},
     title = {Existence and uniqueness of mild solutions for fractional semilinear differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a71/}
}
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Guswanto, Bambang Hendriya; Suzuki, Takashi. Existence and uniqueness of mild solutions for fractional semilinear differential equations. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a71/