Geodesic
Existence of solutions to fractional order ordinary and delay differential equations and applications
Electronic Journal of Differential Equations, Tome 2011 (2011).

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

Summary: In this article, we discuss the existence and uniqueness of solution to fractional order ordinary and delay differential equations. We apply our results on the single species model of Lotka Volterra type. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle and then Krasnoselskii's fixed point theorem to show the existence and uniqueness of the solution under certain conditions. Moreover, we prove that the solution can be extended to maximal interval of existence.
Classification : 34K40, 34K14
Keywords: fractional differential equation, fixed point theorems, maximum interval of existence 
@article{EJDE_2011__2011__a90,
     author = {Abbas, Syed},
     title = {Existence of solutions to fractional order ordinary and delay differential equations and applications},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a90/}
}
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Abbas, Syed. Existence of solutions to fractional order ordinary and delay differential equations and applications. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a90/