scholarly journals Hyers–Ulam Stability for Cayley Quantum Equations and Its Application to h-Difference Equations

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Difference Equations ◽  
Variable Coefficient ◽  
Ulam Stability ◽  
Quantum Equation ◽  
Specific Variable ◽  
Quantum Equations

AbstractThe main purpose of this study is to clarify the Hyers–Ulam stability (HUS) for the Cayley quantum equation. In addition, the result obtained for all parameters is applied to HUS of h-difference equations with a specific variable coefficient using a new transformation.

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 Ulam stability for nonautonomous quantum equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Coefficient Function ◽  
Ulam Stability ◽  
Order Linear ◽  
Quantum Equation ◽  
First Order ◽  
Quantum Equations

AbstractWe establish the Ulam stability of a first-order linear nonautonomous quantum equation with Cayley parameter in terms of the behavior of the nonautonomous coefficient function. We also provide details for some cases of Ulam instability.

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

2020 ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Ulam Stability ◽  
Quantum Equations

scholarly journals Dual Quantum Mechanics and Its Electromagnetic Analog

2018 ◽  
Author(s):  
Arbab Arbab
Keyword(s):  
Electromagnetic Field ◽  
Telegraph Equation ◽  
Matter Wave ◽  
Quantum Equation ◽  
Particular Solution ◽  
Moving Particle ◽  
Quantum Force ◽  
Quantum Equations ◽  
Dual Quantum ◽  
Wave Momentum

An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation keeping the form of the particle fixed but decaying its amplitude. An analogy with Maxwellian equations is presented. Massive electromagnetic field will satisfy a quantum Telegraph equation instead of a pure wave equation. This equation resembles the motion of the electromagnetic field in a conducting medium. With a particular setting of the scalar and vector wavefunctions, the dual quantum equations are found to yield the quantized Maxwell's equations. The total energy of the particle is related to the phase velocity ($v_p$) of the wave representing it by $E=p\,|v_p|$, where $p$ is the matter wave momentum. A particular solution which describes the process under which the particle undergoes a creation and annihilation is derived. The force acting on the moving particle is expressed in a dual Lorentz-like form. If the particle moves like a fluid, a dissipative (drag) quantum force will arise.

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