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7: Paper Source PDF document

Paper's Title:

Reduced Generalized Combination Synchronization Between Two n-Dimensional Integer-Order Hyperchaotic Systems and One m-Dimensional Fractional-Order Chaotic System


Smail Kaouache, Mohammed Salah Abdelouahab and Rabah Bououden

Laboratory of Mathematics and their interactions,
Abdelhafid Boussouf University Center, Mila.


This paper is devoted to investigate the problem of reduced generalized combination synchronization (RGCS) between two n-dimensional integer-order hyperchaotic drive systems and one m-dimensional fractional-order chaotic response system. According to the stability theorem of fractional-order linear system, an active mode controller is proposed to accomplish this end. Moreover, the proposed synchronization scheme is applied to synchronize three different chaotic systems, which are the Danca hyperchaotic system, the modified hyperchaotic Rossler system, and the fractional-order Rabinovich-Fabrikant chaotic system. Finally, numerical results are presented to fit our theoretical analysis.

2: Paper Source PDF document

Paper's Title:

Some interesting properties of finite continuous CesÓro operators


Abdelouahab Mansour and Abderrazak Hechifa

Operator theory laboratory (LABTHOP),
Eloued University,

Mathematics Department,
Faculty of Science,
Badji Mokhtar University, -Annaba,


A complex scalar λ is called an extended eigenvalue of a bounded linear operator T on a complex Banach space if there is a nonzero operator X such that TX = λ XT, the operator X is called extended eigenoperator of T corresponding to the extended eigenvalue λ.

In this paper we prove some properties of extended eigenvalue and extended eigenoperator for C1 on Lp([0,1]), where C1 is the CesÓro operator defined on the complex Banach spaces Lp([0 , 1])  for 1<p<∞ by the expression

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