Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel

2019 ◽  
pp. 293-308 ◽  
Author(s):  
K. M. Saad ◽  
J. F. Gómez-Aguilar ◽  
A. Atangana ◽  
R. F. Escobar-Jiménez
Keyword(s):  
Fractional Derivative ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Singular Kernel ◽  
Fractional Reaction

Observer-based output feedback control design for a coupled system of fractional ordinary and reaction–diffusion equations

2020 ◽  
Author(s):  
Shadi Amiri ◽  
Mohammad Keyanpour ◽  
Asadollah Asaraii
Keyword(s):  
Differential Equation ◽  
Output Feedback ◽  
Closed Loop ◽  
Output Feedback Control ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Reaction Diffusion Equations ◽  
Backstepping Method ◽  
Neumann Type ◽  
Fractional Reaction

Abstract In this paper, we investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional reaction–diffusion (FRD) equation where the interconnections are of Neumann type. We exploit the partial differential equation backstepping method for designing a controller, which guarantees the Mittag–Leffler stability of the FODE-FRD cascade. Moreover, we propose an observer that is Mittag–Leffler convergent. Also, we propose an output feedback boundary controller, and we prove that the closed-loop FODE-FRD system is Mittag–Leffler stable in the sense of the corresponding norm. Finally, numerical simulations are presented to verify the results.

scholarly journals A Numerical Approach of a Time Fractional Reaction–Diffusion Model with a Non-Singular Kernel

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1653
Author(s):  
Tayyaba Akram ◽  
Muhammad Abbas ◽  
Ajmal Ali ◽  
Azhar Iqbal ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Technique ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Singular Kernel ◽  
Stability And Convergence ◽  
Theoretical Interpretation ◽  
Numerical Techniques ◽  
B Spline ◽  
Reaction Diffusion Model ◽  
Fractional Reaction

The time–fractional reaction–diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo–Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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