Geodesic
Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions
Electronic journal of differential equations, Tome 2009 (2009)
In this article we study the fractional semilinear mixed Volterra-Fredholm integrodifferential equation

$ \frac{d^{\alpha }x(t)}{dt^{\alpha }} =Ax(t)+f\Big(t,x(t), \int_{t_0}^tk(t,s,x(s))ds,\int_{t_0}^{T}h(t,s,x(s))ds\Big) , $

where $t\in [t_0,T], t_0\geq 0, 0\alpha 1$, and $f$ is a given function. We prove the existence and uniqueness of solutions to this equation, with a nonlocal condition.
Classification : 45J05, 26A33, 34A12
Keywords: fractional integrodifferential equations, mild solution, nonlocal condition, Banach fixed point 
@article{EJDE_2009__2009__a164,
     author = {Matar,  Mohammed M.},
     title = {Existence and uniqueness of solutions to fractional semilinear mixed {Volterra-Fredholm} integrodifferential equations with nonlocal conditions},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1179.45012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a164/}
}
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TI  - Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions
JO  - Electronic journal of differential equations
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VL  - 2009
UR  - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a164/
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%0 Journal Article
%A Matar,  Mohammed M.
%T Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions
%J Electronic journal of differential equations
%D 2009
%V 2009
%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a164/
%G en
%F EJDE_2009__2009__a164
Matar,  Mohammed M. Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a164/