FRACTIONAL LANGEVIN EQUATIONS WITH INFINITE-POINT BOUNDARY CONDITION: APPLICATION TO FRACTIONAL HARMONIC OSCILLATOR

Lamya Almaghamsi; Ahmed Salem

doi:10.11948/20230124

2023 Volume 13 Issue 6

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Lamya Almaghamsi, Ahmed Salem. FRACTIONAL LANGEVIN EQUATIONS WITH INFINITE-POINT BOUNDARY CONDITION: APPLICATION TO FRACTIONAL HARMONIC OSCILLATOR[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3504-3523. doi: 10.11948/20230124

Citation:

Lamya Almaghamsi, Ahmed Salem. FRACTIONAL LANGEVIN EQUATIONS WITH INFINITE-POINT BOUNDARY CONDITION: APPLICATION TO FRACTIONAL HARMONIC OSCILLATOR[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3504-3523. doi: 10.11948/20230124

FRACTIONAL LANGEVIN EQUATIONS WITH INFINITE-POINT BOUNDARY CONDITION: APPLICATION TO FRACTIONAL HARMONIC OSCILLATOR

Lamya Almaghamsi^1,,
Ahmed Salem^2, ,

1.
Department of Mathematics and Statistics, College of Science, University of Jeddah, P.O. Box: 80327 Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box: 80203, Jeddah 21589, Saudi Arabia

Author Bio: Email: lalmaghamsi@uj.edu.sa(L. Almaghamsi)
Corresponding author: Email: asaalshreef@kau.edu.sa(A. Salem)
Fund Project: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under Grant no. (KEP-PhD-57-130-42). The authors, therefore, acknowledge with thanks DSR technical and financial support

Abstract

Abstract

The current study is concerned with the existence and uniqueness of the solution to the Langevin equation of two separate fractional orders. With the infinite-point boundary condition, the boundary value problem is studied. The Banach contraction principle, Leray-nonlinear Schauder's alternative, and Leray-Schauder degree theorems are all implemented. A numerical example is presented to demonstrate the accuracy of our results. In addition, as an application of our results, the mean and variance of a fractional harmonic oscillator with the undamped angular frequency of the oscillator under the effect of a random force described as Gaussian colored noise are calculated.
- Fractional Langevin equations /
- fixed point theorem /
- existence and uniqueness /
- infinite-point boundary condition /
- mean /
- and variance
MSC: 26A33, 34A08, 34A12

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References

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