Skip to main content
SpringerLink
Log in

Fermi–Walker conformable connection and the evolution of the conformable magnetically driven particles

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

We conduct a thorough exploration of the magnetic flows and physical dynamics exhibited by point charged particles in three-dimensional ordinary space. Our methodology is grounded in the application of conformable methods. Initially, we refine the general treatment to derive velocity and acceleration vector fields for point particles traversing conformable curves under the influence of distinct force fields. Subsequently, our inquiry extends into the realm of magnetism, where we investigate various types of dynamical magnetic curves that emerge from characterizing the movement of charged particles along conformable curves. In addition to this, we introduce the Fermi–Walker conformable derivative and provide an alternative representation for a unit-speed conformable curve by leveraging the Fermi–Walker connection. Throughout the entirety of the paper, we establish a meaningful correlation between the consistent motion of conformable charged particles and the trajectories dictated by specific external forces within the \(\alpha \)-Frenet–Serret frame. The application of fractional calculus plays a pivotal role in our investigations, a facet we meticulously delve into in the paper. This work significantly contributes to an enhanced comprehension of magnetic phenomena and dynamics, offering valuable insights into the behavior of charged particles within conformable frameworks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. D Kumar, P A Ravi and S Jagdev J. Comput. Appl. Math. 339 405 (2018)

    Article  MathSciNet  Google Scholar 

  2. J Singh, D Kumar and D Baleanu Chaos Interdiscip. J. Nonlinear Sci. 27 103113 (2017)

    Article  Google Scholar 

  3. D Kumar, J Singh and D Baleanu Nonlinear Dyn. 91 307 (2018)

    Article  Google Scholar 

  4. D Zhao, J Singh, D Kumar, and S Rathore J. Nonlinear Sci. Appl. 10 (2017)

  5. M Hajipour, A Jajarmi, and D Baleanu J. Comput. Nonlinear Dyn.13 (2018)

  6. D Baleanu, A Jajarmi, J H Asad and T Blaszczyk Acta Phys. Pol. A 131 1561 (2017)

    Article  ADS  Google Scholar 

  7. D Kumar, J Singh and D Baleanu Phys. Stat. Mech. Appl. 492 155 (2018)

    Article  Google Scholar 

  8. H Sun, X Hao, Y Zhang and D Baleanu Phys. Stat. Mech. Appl. 468 590 (2017)

    Article  Google Scholar 

  9. D Baleanu, A Jajarmi and M Hajipour J. Optim. Theory Appl. 175 718 (2017)

    Article  MathSciNet  Google Scholar 

  10. A Ebaid Appl. Math. Modell. 35 1231 (2011)

    Article  MathSciNet  Google Scholar 

  11. B Ahmad, H Batarfi, J J Nieto, Ó Otero-Zarraquiños and W Shammakh Adv. Diff. Equ. 2015 1 (2015)

    Article  Google Scholar 

  12. J R Garcia, M G Calderon, J M Ortiz, D Baleanu, and C S V de Santiago Proc. Roman. Acad. A 14 42 (2013)

  13. J Rosales, M Guía, F Gómez and F Aguilar J. Martínez Open Phys. 12 517 (2014)

    ADS  Google Scholar 

  14. M Ekici, M Mirzazadeh, M Eslami, Q Zhou, S P Moshokoa, A Biswas and M Belic Optik 127 10659 (2016)

    Article  ADS  Google Scholar 

  15. M S Osman, A Korkmaz, H Rezazadeh, M Mirzazadeh, M Eslami and Q Zhou Chin. J. Phys. 56 2500 (2018)

    Article  ADS  Google Scholar 

  16. F M Alharbi, D Baleanu and A Ebaid Chin. J. Phys. 58 18 (2019)

    Article  ADS  Google Scholar 

  17. M Barros, A Romero, J L Cabrerizo and M Fernández J. Math. Phys. 46 112905 (2005)

    Article  ADS  Google Scholar 

  18. M Barros, J L Cabrerizo, M Fernández and A Romero J. Math. Phys. 48 082904 (2007)

    Article  ADS  Google Scholar 

  19. S Manoff Int. J. Mod. Phys. A13 4289 (1998)

  20. D Bini, F de Felice and R T Jantzen Class. Quant. Gravity 16 2105 (1999)

    Article  ADS  Google Scholar 

  21. J W Maluf and F F Faria Ann. Phys. 17 326 (2008)

    Article  MathSciNet  Google Scholar 

  22. F Karakuş and Y Yayli Int. J. Geomet. Methods Mod. Phys. 9 1250066 (2012)

    Article  MathSciNet  Google Scholar 

  23. T Körpinar, R C Demirkol and V Asil Indian J. Phys. 95 2393 (2021)

    Article  ADS  Google Scholar 

  24. T Korpinar, D Baleanu, Z Korpinar and M Inc J. Geomet. Phys. 170 104353 (2021)

    Article  Google Scholar 

  25. R Khalil, M Al Horani, A Yousef and M Sababheh J. comput. Appl. Math. 264 65 (2014)

    Google Scholar 

  26. E D Bloch A first course in geometric topology and differential geometry (Springer Science, Business Media Chapter 4 (2011)

  27. B Yilmaz Optik247 168026 (2021)

  28. T Korpinar and R C Demirkol Inte. J. Geomet. Methods Mod. Phys. 15 1850020 (2018)

    Article  ADS  Google Scholar 

  29. T Körpınar and R C Demirkol Int. J. Geomet. Methods Mod. Phys. 15 1850184 (2018)

    Article  ADS  Google Scholar 

  30. F González-Cataldo, G Gutiérrez and J M Yáñez Am. J. Phys. 85 108 (2017)

    Article  ADS  Google Scholar 

  31. G Calvaruso, M I Munteanu and A Perrone J. Math. Anal. Appl. 426 423 (2015)

    Article  Google Scholar 

  32. Z Özdemir, İ Gök, Y Yayli and F N Ekmekci Turk. J. Math. 39 412 (2015)

    Article  Google Scholar 

  33. S L Druţă-Romaniuc and M I Munteanu Nonlinear Anal. Real World Appl. 14 383 (2013)

    Google Scholar 

  34. J I Inoguchi, M I Munteanu and A I Nistor Anal. Math. Phys. 9 43 (2019)

    Article  ADS  Google Scholar 

  35. Z Erjavec and J I Inoguchi Res. Math. 75 1 (2020)

    ADS  MathSciNet  Google Scholar 

  36. T Körpinar and R C Demirkol Optik 200 163334 (2020)

    Google Scholar 

  37. T Korpinar and R C Demirkol J. Mod. Optics 66 857 (2019)

    Article  ADS  Google Scholar 

  38. H Ceyhan, Z Özdemir, İ Gök and F N Ekmekci Eur. Phys. J. Plus 135 1 (2020)

    Article  ADS  Google Scholar 

  39. N Ertuğ Gürbüz Int. J. Geomet. Methods Mod. Phys.18 2150122-57 (2021)

  40. N Ertuğ Gürbüz Optik247 167989 (2021)

  41. D De la Fuente and A Romero Gen. Relativ. Gravit. 47 1–13 (2015)

    Article  Google Scholar 

  42. D De la Fuente, A Romero and P J Torres J. Math. Phys. 56 112501 (2015)

    Article  ADS  Google Scholar 

  43. D De la Fuente, A Romero and P J Torres Class. Quant. Gravity 34 125016 (2017)

    Article  ADS  Google Scholar 

  44. R Khalil, M Al Horani, A Yousef and M Sababheh J. Comput. Appl. Math. 264 65 (2014)

    Google Scholar 

  45. Z Korpinar, F Tchier, M Inc, L Ragoub and M Bayram Res. Phys. 14 102395 (2019)

    Article  Google Scholar 

  46. Z Odibat and S Momani Appl. Math. Model. 32 28 (2008)

    Article  Google Scholar 

  47. M Mirzazadeh, M Eslami, D Milovic and A Biswas Optik 125 5480 (2014)

    Article  Google Scholar 

  48. A Biswas, Q Zhou, S P Moshokoa, H Triki, M Belic and R T Alqahtani Optik 145 14 (2017)

    Google Scholar 

  49. H O Bakodah, A A Al Qarni, M A Banaja, Q Zhou, S P Moshokoa and A Biswas Optik 130 1115 (2017)

  50. H Triki, A Biswas, S P Moshokoa and M Belic Optik 128 63 (2017)

    Article  ADS  Google Scholar 

  51. A Biswas, Y Yildirim, E Yasar, H Triki, A S Alshomrani, M Z Ullah and M Belic Optik160 44 (2018)

  52. A Biswas J. Optics49 580 (2020)

  53. A J A M Jawad, M Mirzazadeh, Q Zhou and A Biswas Superlattices Microstruct. 105 1 (2017)

    Article  ADS  Google Scholar 

Download references

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

  1. Department of Mathematics, Muş Alparslan University, 49250, Muş, Turkey

    Talat Körpinar & Rıdvan Cem Demirkol

  2. Department of Administration, Muş Alparslan University, 49250, Muş, Turkey

    Zeliha Körpınar

Authors
  1. Talat Körpinar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rıdvan Cem Demirkol
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zeliha Körpınar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors wrote the paper jointly and contributed equally to this work. All authors read and approved the final version of the manuscript.

Corresponding author

Correspondence to Rıdvan Cem Demirkol.

Ethics declarations

Conflict of interest

All authors confirm that there is no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Körpinar, T., Demirkol, R.C. & Körpınar, Z. Fermi–Walker conformable connection and the evolution of the conformable magnetically driven particles. Indian J Phys (2024). https://doi.org/10.1007/s12648-023-03053-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12648-023-03053-8

Keywords

Mathematics Subject Classification

Search

Navigation