PlumX Metrics
Embed PlumX Metrics

Stability analysis of tempered fractional nonlinear Mathieu type equation model of an ion motion with octopole-only imperfections

Mathematical Methods in the Applied Sciences, ISSN: 1099-1476, Vol: 46, Issue: 8, Page: 9542-9554
2023
  • 0
    Citations
  • 0
    Usage
  • 1
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

Article Description

The development of laser-based cooling and spectroscopic methods has produced unprecedented growth in the ion trapping industry. Mathieu equation, a differential equation with periodic coefficients, is employed to develop models of ion motions under the influence of fields. Ion traps with octopole field is described with nonlinear Mathieu equation with cubic term. This article aims at considering motion of ions under the electric potential with negative octopole field with damping caused by the collision of the ions with Helium buffer gas modeled with tempered fractional derivative. Schaefer's fixed point theorem and Banach's contraction principle are employed to establish the existence of unique solution for the considered tempered fractional nonlinear Mathieu equation model of an ion motion. Further, the analysis of stability is performed in the sense of Hyers and Ulam. The feasibility of the obtained theoretical results are numerically confirmed for suitable parametric values, and simulations are performed supporting them.

Bibliographic Details

Jehad Alzabut; A. George Maria Selvam; Dhakshinamoorthy Vignesh; Sina Etemad; Shahram Rezapour

Wiley

Mathematics; Engineering

Provide Feedback

Have ideas for a new metric? Would you like to see something else here?Let us know