Geodesic
Existence and uniqueness of mild solutions for fractional semilinear differential equations
Electronic journal of differential equations, Tome 2015 (2015)
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},
     year = {2015},
     volume = {2015},
     zbl = {1329.34008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a71/}
}
TY  - JOUR
AU  - Guswanto,  Bambang Hendriya
AU  - Suzuki,  Takashi
TI  - Existence and uniqueness of mild solutions for fractional semilinear differential equations
JO  - Electronic journal of differential equations
PY  - 2015
VL  - 2015
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a71/
LA  - en
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ER  - 
%0 Journal Article
%A Guswanto,  Bambang Hendriya
%A Suzuki,  Takashi
%T Existence and uniqueness of mild solutions for fractional semilinear differential equations
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a71/
%G en
%F EJDE_2015__2015__a71
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/