scholarly journals Ulam-Hyers stability results for a novel nonlinear Nabla Caputo fractional variable-order difference system

2021 ◽  
Keyword(s):  
Variable Order ◽  
Difference System ◽  
Order Difference ◽  
Stability Results

scholarly journals Dynamics of a second-order nonlinear difference system with exponents

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
D. S. Dilip ◽  
Smitha Mary Mathew
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Second Order ◽  
Difference System ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference

AbstractIn this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of the positive solutions of the second-order difference system $$\begin{aligned} x_{n+1}&= \alpha _1 + a e ^{-x_{n-1}} + b y_{n} e ^{-y_{n-1}},\\ y_{n+1}&= \alpha _2 +c e ^{-y_{n-1}}+ d x_{n} e ^{-x_{n-1}} \quad n=0,1,2,\ldots \end{aligned}$$ x n + 1 = α 1 + a e - x n - 1 + b y n e - y n - 1 , y n + 1 = α 2 + c e - y n - 1 + d x n e - x n - 1 n = 0 , 1 , 2 , … where $$\alpha _1, \alpha _2, a, b , c,d$$ α 1 , α 2 , a , b , c , d are positive real numbers and the initial conditions $$x_{-1},x_0, y_{-1}, y_0$$ x - 1 , x 0 , y - 1 , y 0 are arbitrary nonnegative numbers.

scholarly journals Coupled implicit Caputo fractional q-difference systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Bessem Samet ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Difference System ◽  
Uniqueness Of Solutions ◽  
Difference Systems ◽  
Stability Results

AbstractThis paper deals with some existence, uniqueness, and Ulam stability results for a coupled implicit Caputo fractional q-difference system in Banach and generalized Banach spaces. Some applications are made of some fixed point theorems for the existence and uniqueness of solutions. Next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Some illustrative examples are given in the last section.

scholarly journals Analog Realization of a Fractional Recursive Variable-Type and Order Operator for a Particular Switching Strategy

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 855
Author(s):  
Dominik Sierociuk ◽  
Michal Macias ◽  
Wiktor Malesza ◽  
Michał Sławomir Wiraszka
Keyword(s):  
Experimental Validation ◽  
Hardware Implementation ◽  
Difference Operator ◽  
Variable Order ◽  
Practical Realization ◽  
Analog Model ◽  
Order Difference ◽  
Variable Type ◽  
Proposed Model ◽  
Type Variable

In this paper, we propose a method of practical realization and an actual, physical hardware implementation of a fractional variable-type and order difference operator that switches between two (i.e., B - and D -type) variable-order definitions. After the theoretical model of such a switch, we report the experimental validation on an analog model to prove its adequacy. The tests prove with great certainty that the proposed model and the realization behave correctly. They also let the authors assume that the proposed method is the only one suitable for this case, based on the counterexamples presented.

scholarly journals First order difference system- existence and uniqueness

1997 ◽  
Vol 125 (12) ◽  
pp. 3533-3539 ◽  
Author(s):  
K. N. Murty ◽  
P. V. S. Anand ◽  
V. Lakshmi Prasannam
Keyword(s):  
Existence And Uniqueness ◽  
Difference System ◽  
Order Difference ◽  
First Order

scholarly journals On the Global Asymptotic Stability of Solutions of Some Difference Equations with Intrinsic Initial Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Vasile Berinde
Keyword(s):  
Global Stability ◽  
Difference Equations ◽  
Software Package ◽  
Numerical Experiments ◽  
Initial Conditions ◽  
Remarkable Feature ◽  
Order Difference ◽  
First Order ◽  
The Stability ◽  
Stability Results

Our aim in this paper is to study the asymptotic global stability of the positive solutions for a class of first-order nonlinear difference equations with a remarkable feature: the initial conditions are intrinsic and not explicitly given. Global stability results are obtained in a particular case and then for a general class of first-order difference equations. We also provide the results of some numerical experiments obtained by the mini software package FIXPOINT to illustrate asymptotic global stability as well as the rate of convergence. To the best of our knowledge, our approach is the first one in the literature on the stability of difference equations without explicit initial conditions and might generate an interesting new direction of further studies.

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