HYERS-ULAM STABILITY FOR SEQUENTIAL FRACTIONAL ORDER h-DIFFERENCE EQUATIONS

2020 ◽  
Vol 29 (1) ◽  
Author(s):  
Xiang Liu ◽  
Baoguo Jia ◽  
Douglas Anderson
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Ulam Stability

scholarly journals Ulam stability results for boundary value problem of fractional difference equations

2020 ◽  
pp. 219-230
Author(s):  
A. George Maria Selvam ◽  
R. Dhineshbabu
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Boundary Value ◽  
Ulam Stability ◽  
Fractional Difference ◽  
Stability Results

Boundary value problems have wide applications in science and technology. This paper is concerned with various kinds of Ulam stability analysis for the nonlinear discrete boundary value problem of fractional order $\sigma\in(2,3]$ with Riemann-Liouville fractional difference operator. Finally, some examples are presented to illustrate the main results.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

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

scholarly journals Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Mary Jacintha ◽  
Abdullah Özbekler
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Fractional Operators ◽  
Damping Term ◽  
Fractional Difference ◽  
Riccati Technique ◽  
Order Difference ◽  
Numerical Examples ◽  
Positive Integers

The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

scholarly journals A fixed point approach to the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation

2016 ◽  
Vol 14 (1) ◽  
pp. 237-246 ◽  
Author(s):  
Nasrin Eghbali ◽  
Vida Kalvandi ◽  
John M. Rassias
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fractional Order ◽  
Fractional Integral ◽  
Compact Interval ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Delay Integral Equation ◽  
Fractional Integral Equation

AbstractIn this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.

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