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Weak solution for fractional order integral equations in reflexive Banach spaces

In: Mathematica Slovaca, vol. 55, no. 2
Hussein A. H. Salem - Wagdy Gomaa El-Sayed
Detaily:
Rok, strany: 2005, 169 - 181
O článku:
In this paper, we define the fractional order Pettis-integral operator in reflexive Banach spaces and we investigate the properties of such operator. A fixed point theorem is used to establish an existence result for the nonlinear Pettis-fractional order integral equation of the following type

$$ x(t)=g(t)+λ Iαf(t,x(t)) ,    t\in [0,1] , 0<α <1 . $$

Moreover, the existence of a solutions for the Cauchy problem

$$ ((d x) / (d t)) = f(t,Dβ x(t)),    t\in [0,1] , 0< β<1 , x(0) = x0 , $$

is proved.
Ako citovať:
ISO 690:
Salem, H., El-Sayed, W. 2005. Weak solution for fractional order integral equations in reflexive Banach spaces. In Mathematica Slovaca, vol. 55, no.2, pp. 169-181. 0139-9918.

APA:
Salem, H., El-Sayed, W. (2005). Weak solution for fractional order integral equations in reflexive Banach spaces. Mathematica Slovaca, 55(2), 169-181. 0139-9918.