scholarly journals Centralized and Decentralized Data-Sampling Principles for Outer-Synchronization of Fractional-Order Neural Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jin-E Zhang
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Data Sampling ◽  
Outer Synchronization ◽  
Numerical Example ◽  
State Dependent ◽  
Fractional Differential ◽  
Theoretical Results

This paper aims to investigate the outer-synchronization of fractional-order neural networks. Using centralized and decentralized data-sampling principles and the theory of fractional differential equations, sufficient criteria about outer-synchronization of the controlled fractional-order neural networks are derived for structure-dependent centralized data-sampling, state-dependent centralized data-sampling, and state-dependent decentralized data-sampling, respectively. A numerical example is also given to illustrate the superiority of theoretical results.

scholarly journals On Stability of Nonautonomous Perturbed Semilinear Fractional Differential Systems of Order α∈(1,2)

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed M. Matar ◽  
Esmail S. Abu Skhail
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Protected Area ◽  
Marine Protected Area ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Stability Results

We study the Mittag-Leffler and class-K function stability of fractional differential equations with order α∈(1,2). We also investigate the comparison between two systems with Caputo and Riemann-Liouville derivatives. Two examples related to fractional-order Hopfield neural networks with constant external inputs and a marine protected area model are introduced to illustrate the applicability of stability results.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1755
Author(s):  
M. S. Al-Sharif ◽  
A. I. Ahmed ◽  
M. S. Salim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

scholarly journals Stability analysis of linear conformable fractional differential equations system with time delays

2019 ◽  
Vol 38 (6) ◽  
pp. 159-171 ◽  
Author(s):  
Vahid Mohammadnezhad ◽  
Mostafa Eslami ◽  
Hadi Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Euler’S Method ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we first study stability analysis of linear conformable fractional differential equations system with time delays. Some sufficient conditions on the asymptotic stability for these systems are proposed by using properties of the fractional Laplace transform and fractional version of final value theorem. Then, we employ conformable Euler’s method to solve conformable fractional differential equations system with time delays to illustrate the effectiveness of our theoretical results

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