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

Shorouk Al-IssaAhmed Mohamed Ahmed El-Sayed — 2009

Commentationes Mathematicae

In this paper we study the global existence of positive integrable solution for the nonlinear integral inclusion of fractional order x ( t ) p ( t ) + I α F 1 ( t , I β f 2 ( t , x ( ϕ ( t ) ) ) ) , t ( 0 , 1 ) . As an application the global existence of the solution for the initial-value problem of the arbitrary (fractional) orders differential inclusion d x ( t ) d t p ( t ) + I 1 ( t , D ( t ) ) ) , a.e. t g t 0 will be studied.

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