scholarly journals Solving Fractional Difference Equations Using the Laplace Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Li Xiao-yan ◽  
Jiang Wei
Keyword(s):  
Laplace Transform ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Initial Value ◽  
Laplace Transform Method ◽  
Fractional Difference ◽  
Transform Method ◽  
Fractional Difference Equations ◽  
The Laplace Transform ◽  
Linear And Nonlinear

We discuss the Laplace transform of the Caputo fractional difference and the fractional discrete Mittag-Leffer functions. On these bases, linear and nonlinear fractional initial value problems are solved by the Laplace transform method.

Some further results of the laplace transform for variable–order fractional difference equations

2019 ◽  
Vol 22 (6) ◽  
pp. 1641-1654 ◽  
Author(s):  
Dumitru Baleanu ◽  
Guo–Cheng Wu
Keyword(s):  
Laplace Transform ◽  
Exact Solutions ◽  
Difference Equations ◽  
Response Analysis ◽  
Variable Order ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
The Laplace Transform ◽  
Linear Differential ◽  
Time Systems

Abstract The Laplace transform is important for exact solutions of linear differential equations and frequency response analysis methods. In comparison with the continuous–time systems, less results can be available for fractional difference equations. This study provides some fundamental results of two kinds of fractional difference equations by use of the Laplace transform. Some discrete Mittag–Leffler functions are defined and their Laplace transforms are given. Furthermore, a class of variable–order and short memory linear fractional difference equations are proposed and the exact solutions are obtained.

scholarly journals A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Chunlin Su ◽  
Bin Zhen ◽  
Zigen Song
Keyword(s):  
Laplace Transform ◽  
Chaotic Behavior ◽  
Integral Form ◽  
Nonlinear Coupling ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform ◽  
Analytical Criterion ◽  
Linear And Nonlinear ◽  
The Stability

In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons.

scholarly journals On Solution of First Order Initial Value Problems using Laplace Transform in Fuzzy Environment

2021 ◽  
Vol 7 (2) ◽  
pp. 21-29
Author(s):  
Abubakar Terrang ◽  
◽  
Awumtiya Isa ◽  
Felix Bakare ◽  
Patience Iliya ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Initial Value ◽  
Laplace Transform Method ◽  
Transform Method ◽  
First Order ◽  
Fuzzy Environment ◽  
Fuzzy Function

This study aimed at solving a nonhomogeneous linear first order initial value problem by means of Laplace transform method in fuzzy environment. The conditions for a fuzzy function to be H−differentiable and gH−differentiability are well established. Finally, example is constructed to test the applicability or otherwise of the established results.

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