scholarly journals A New Type of Identification Problems: Optimizing the Fractional Order in a Nonlocal Evolution Equation

2017 ◽  
Vol 55 (1) ◽  
pp. 70-93 ◽  
Author(s):  
Jürgen Sprekels ◽  
Enrico Valdinoci
Keyword(s):  
Evolution Equation ◽  
Fractional Order ◽  
Identification Problems ◽  
Nonlocal Evolution Equation ◽  
New Type

scholarly journals Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 481 ◽  
Author(s):  
Zhonghui Li ◽  
Tongshui Xia ◽  
Cuimei Jiang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Order Complex ◽  
Order Error ◽  
New Type ◽  
Modified Projective Synchronization ◽  
The Stability ◽  
Complex Chaotic Systems

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

Existence and Asymptotic Properties of Solutions of a Nonlocal Evolution Equation Modeling Cell-Cell Adhesion

2010 ◽  
Vol 42 (4) ◽  
pp. 1784-1804 ◽  
Author(s):  
Janet Dyson ◽  
Stephen A. Gourley ◽  
Rosanna Villella-Bressan ◽  
Glenn F. Webb
Keyword(s):  
Cell Adhesion ◽  
Evolution Equation ◽  
Asymptotic Properties ◽  
Equation Modeling ◽  
Nonlocal Evolution Equation ◽  
Cell Cell

scholarly journals Numerical Approximations for a Nonlocal Evolution Equation

2011 ◽  
Vol 49 (5) ◽  
pp. 2103-2123 ◽  
Author(s):  
Mayte Pérez-LLanos ◽  
Julio D. Rossi
Keyword(s):  
Evolution Equation ◽  
Numerical Approximations ◽  
Nonlocal Evolution Equation

Sixth-Kind Chebyshev Spectral Approach for Solving Fractional Differential Equations

2019 ◽  
Vol 20 (2) ◽  
pp. 191-203 ◽  
Author(s):  
W. M. Abd-Elhameed ◽  
Y. H. Youssri
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Symmetric Functions ◽  
Numerical Algorithms ◽  
Initial Boundary ◽  
Algebraic Equations ◽  
Fractional Order Differential Equations ◽  
New Type ◽  
Connection Formulae

AbstractThe basic aim of this paper is to develop new numerical algorithms for solving some linear and nonlinear fractional-order differential equations. We have developed a new type of Chebyshev polynomials, namely, Chebyshev polynomials of sixth kind. This type of polynomials is a special class of symmetric orthogonal polynomials, involving four parameters that were constructed with the aid of the extended Sturm–Liouville theorem for symmetric functions. The proposed algorithms are basically built on reducing the fractional-order differential equations with their initial/boundary conditions to systems of algebraic equations which can be efficiently solved. The new proposed algorithms are supported by a detailed study of the convergence and error analysis of the sixth-kind Chebyshev expansion. New connection formulae between Chebyshev polynomials of the second and sixth kinds were established for this study. Some examples were displayed to illustrate the efficiency of the proposed algorithms compared to other methods in literature. The proposed algorithms have provided accurate results, even using few terms of the proposed expansion.

A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 351-359
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Abdulrahman Karouma ◽  
Salem Abdelmalek
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Projective Synchronization ◽  
The Novel ◽  
Fractional Order Systems ◽  
Function Projective Synchronization ◽  
Novel Approach ◽  
Full State ◽  
Hybrid Function ◽  
New Type

AbstractReferring to incommensurate fractional-order systems, this paper proposes a new type of chaos synchronization by combining full state hybrid function projective synchronization (FSHFPS) and inverse full state hybrid function projective synchronization (IFSHFPS). In particular, based on stability theory of linear integer-order systems and stability theory of linear fractional-order systems, the co-existence of FSHFPS and IFSHFPS between incommensurate fractional chaotic (hyperchaotic) systems is proved. To illustrate the capabilities of the novel approach proposed herein, numerical and simulation results are given.

Sign in / Sign up

Export Citation Format

Share Document