Ulam-Hyers-Rassias Stability and Existence of Solutions to Nonlinear Fractional Difference Equations with Multipoint Summation Boundary Condition

2020 ◽  
Vol 40 (2) ◽  
pp. 589-602 ◽  
Author(s):  
Syed Sabyel Haider ◽  
Mujeeb Ur Rehman
Keyword(s):  
Boundary Condition ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Rassias Stability

scholarly journals Existence and Ulam Stability of Solutions for Discrete Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Fulai Chen ◽  
Yong Zhou
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Boundary Value Problem ◽  
Fractional Difference ◽  
Fractional Difference Equations

We discuss the existence of solutions for antiperiodic boundary value problem and the Ulam stability for nonlinear fractional difference equations. Two examples are also provided to illustrate our main results.

scholarly journals NONLINEAR NEUTRAL CAPUTO-FRACTIONAL DIFFERENCE EQUATIONS WITH APPLICATIONS TO LOTKA-VOLTERRA NEUTRAL MODEL

2021 ◽  
pp. 1475
Author(s):  
Mouataz Billah Mesmouli ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Difference Equations ◽  
Existence Of Solutions ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Neutral Model ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Difference Equations

In this paper, we consider a nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of solutions is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in <cite>Azabut</cite>.

scholarly journals Existence of local solutions for fractional difference equations with left focal boundary conditions

2021 ◽  
Vol 24 (1) ◽  
pp. 324-331
Author(s):  
Johnny Henderson ◽  
Jeffrey T. Neugebauer
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Real Number ◽  
Natural Number ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation ◽  
Local Solutions

Abstract For 1 < ν ≤ 2 a real number and T ≥ 3 a natural number, conditions are given for the existence of solutions of the νth order Atıcı-Eloe fractional difference equation, Δ ν y(t) + f(t + ν − 1, y(t + ν − 1)) = 0, t ∈ {0, 1, …, T}, and satisfying the left focal boundary conditions Δy(ν − 2) = y(ν + T) = 0.

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.

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

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