Regional boundary controllability of semilinear subdiffusion Caputo fractional systems

2021 ◽  
Author(s):  
Asmae Tajani ◽  
Fatima-Zahrae El Alaoui ◽  
Ali Boutoulout
Keyword(s):  
Boundary Controllability ◽  
Fractional Systems ◽  
Regional Boundary

scholarly journals Boundary controllability of nonlinear stochastic fractional systems in Hilbert spaces

2018 ◽  
Vol 28 (1) ◽  
pp. 123-133 ◽  
Author(s):  
Rajendran Mabel Lizzy ◽  
Krishnan Balachandran
Keyword(s):  
Hilbert Spaces ◽  
Contraction Mapping ◽  
Control Function ◽  
Sufficient Conditions ◽  
Contraction Mapping Theorem ◽  
Boundary Controllability ◽  
Fractional Systems ◽  
Banach Contraction ◽  
Linear And Nonlinear Systems ◽  
Banach Contraction Mapping

AbstractSufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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