Hyers-Ulam Stability of Difference Equations

2021 ◽  
pp. 193-208
Author(s):  
Arun Kumar Tripathy
Keyword(s):  
Difference Equations ◽  
Ulam Stability

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 Hyers–Ulam Stability for Quantum Equations of Euler Type

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Discrete Dynamics ◽  
Direct Connection ◽  
Ulam Stability ◽  
Arbitrary Integer ◽  
Step Size ◽  
First Order ◽  
Constant Coefficients ◽  
Quantum Equations

Many applications using discrete dynamics employ either q-difference equations or h-difference equations. In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (q-difference) equation of Euler type. In particular, we show a direct connection between quantum equations of Euler type and h-difference equations of constant step size h with constant coefficients and an arbitrary integer order. For equation orders greater than two, the h-difference results extend first-order and second-order results found in the literature, and the Euler-type q-difference results are completely novel for any order. In many cases, the best HUS constant is found.

scholarly journals Hyers-Ulam Stability of Fractional Nabla Difference Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Jagan Mohan Jonnalagadda
Keyword(s):  
Difference Equation ◽  
Laplace Transform ◽  
Difference Equations ◽  
Ulam Stability

We investigate the Hyers-Ulam stability, the generalized Hyers-Ulam stability, and the Fα-Hyers-Ulam stability of a linear fractional nabla difference equation using discrete Laplace transform. We provide a few examples to illustrate the applicability of established results.

ON APPROXIMATE SOLUTIONS OF SOME DIFFERENCE EQUATIONS

2016 ◽  
Vol 95 (3) ◽  
pp. 476-481 ◽  
Author(s):  
JANUSZ BRZDĘK ◽  
PAWEŁ WÓJCIK
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Approximate Solutions ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability

In this paper we present a simple (fixed point) method that yields various results concerning approximate solutions of some difference equations. The results are motivated by the notion of Ulam 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.

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