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Browsing Journals and Conference Proceedings by Author "Abdelmalek, Salem"
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Item Coexistence of some chaos synchronization types in fractional-order differential equations(Texas State University, Department of Mathematics, 2017-05-10) Ouannas, Adel; Abdelmalek, Salem; Bendoukha, SamirReferring to incommensurate and commensurate fractional systems, this article presents a new approach to investigate the coexistence of some synchronization types between non-identical systems characterized by different dimensions and different orders. In particular, the paper shows that complete synchronization (CS), anti-synchronization (AS) and inverse full state hybrid function projective synchronization (IFSHFPS) coexist when synchronizing a three-dimensional master system with a four-dimensional slave system. The approach is based on two new results involving stability theory of linear fractional systems and the fractional Lyapunov method. A number of examples are provided to highlight the applicability of the method.Item Nonexistence of solutions to Cauchy problems for fractional time semi-linear pseudo-hyperbolic systems(Texas State University, Department of Mathematics, 2016-01-12) Abdelmalek, Salem; Bajneed, Maha; Sioud, KhaledWe study Cauchy problems time fractional semi-linear pseudo-hyperbolic equations and systems. Using the method of nonlinear capacity, we show that there are no solutions for certain nonlinearities and initial data. Our work complements the work by Aliev and col. [1,6,7].