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).

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

Summary: 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__a64,
     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},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a64/}
}
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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__a64/