Stability of Fractional Difference Systems with Two Orders

2013 ◽  
pp. 41-52 ◽  
Author(s):  
Małgorzata Wyrwas ◽  
Ewa Girejko ◽  
Dorota Mozyrska ◽  
Ewa Pawłuszewicz
Keyword(s):  
Fractional Difference ◽  
Difference Systems

scholarly journals Convergence of approximate solutions for singular difference systems with maxima

2021 ◽  
Author(s):  
Xiang Liu ◽  
Christopher GOODRICH ◽  
Peiguang Wang
Keyword(s):  
Comparison Theorem ◽  
Upper And Lower Solutions ◽  
Approximate Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Difference System ◽  
Fractional Difference ◽  
Monotone Iterative ◽  
Difference Systems ◽  
Convergence Of Approximate Solutions

In this paper, by introducing a new singular fractional difference comparison theorem, the existence of maximal and minimal quasi-solutions are proved for the singular fractional difference system with maxima combined with the method of upper and lower solutions and the monotone iterative technique. Finally, we give an example to show the validity of the established results.

Some new Gompertz fractional difference equations

2020 ◽  
Vol 13 (4) ◽  
pp. 705-719
Author(s):  
Tom Cuchta ◽  
Brooke Fincham
Keyword(s):  
Difference Equations ◽  
Fractional Difference ◽  
Fractional Difference Equations

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

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