Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders

Shorouk Al-Issa, and Ahmed Mohamed Ahmed El-Sayed. "Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders." Commentationes Mathematicae 49.2 (2009): null. <http://eudml.org/doc/291610>.

@article{ShoroukAl2009,
abstract = {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 \[ \frac\{dx(t)\}\{dt\}\in p(t)+ I^\_1(t,D^(t))),\quad \text\{a.e.\}\ t gt 0 \] will be studied.},
author = {Shorouk Al-Issa, Ahmed Mohamed Ahmed El-Sayed},
journal = {Commentationes Mathematicae},
keywords = {integral inclusion; fractional-calculus; Caratheodory condition; differential inclusion; fixed point theorem},
language = {eng},
number = {2},
pages = {null},
title = {Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders},
url = {http://eudml.org/doc/291610},
volume = {49},
year = {2009},
}

TY - JOUR
AU - Shorouk Al-Issa
AU - Ahmed Mohamed Ahmed El-Sayed
TI - Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders
JO - Commentationes Mathematicae
PY - 2009
VL - 49
IS - 2
SP - null
AB - 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 \[ \frac{dx(t)}{dt}\in p(t)+ I^_1(t,D^(t))),\quad \text{a.e.}\ t gt 0 \] will be studied.
LA - eng
KW - integral inclusion; fractional-calculus; Caratheodory condition; differential inclusion; fixed point theorem
UR - http://eudml.org/doc/291610
ER -