Geodesic
Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders
Commentationes Mathematicae, Tome 49 (2009) no. 2, pp. 171-177.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this paper we study the global existence of positive integrable solution for the nonlinear integral inclusion of fractional order \[ x(t) \in p(t) + I^\alpha F_1 (t, I^\beta f_2 (t, x(\varphi(t)))),\quad t \in (0, 1). \] As an application the global existence of the solution for the initial-value problem of the arbitrary (fractional) orders differential inclusion \[ \frac{dx(t)}{dt}\in p(t)+ I^\alphaF_1(t,D^\gammax(t))),\quad \text{a.e.}\ t gt 0 \] will be studied.
DOI : 10.14708/cm.v49i2.5293
Mots-clés : integral inclusion, fractional-calculus, Caratheodory condition, differential inclusion, fixed point theorem 
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Shorouk Al-Issa; Ahmed Mohamed Ahmed El-Sayed. Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders. Commentationes Mathematicae, Tome 49 (2009) no. 2, pp.  171-177. doi : 10.14708/cm.v49i2.5293. http://geodesic.mathdoc.fr/articles/10.14708/cm.v49i2.5293/

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