Abstract
AbstractIn this paper, we present a comprehensive investigation into the construction of electromagnetic timelike particles within the frame of Minkowski space, employing the Bishop model. Our study involves deriving the fractional derivatives of key Lorentz forces namely $$\Omega (\textbf{t})$$
Ω
(
t
)
, $$\Omega (v_1)$$
Ω
(
v
1
)
, and $$\Omega (v_2)$$
Ω
(
v
2
)
. Furthermore, we delve into the computation of essential normalizing and recursion operators tailored to magnetic vector fields, drawing from the principles outlined in the Bishop model. Additionally, we extend our analysis to determine the Fermi–Walker (FW) fractional derivatives, which play a crucial role in understanding the behavior and dynamics of the normalizing and recursion operators. Through this thorough exploration, we aim to provide valuable insights into the electromagnetic properties of timelike particles within the context of Minkowski space.
Publisher
Springer Science and Business Media LLC
Reference36 articles.
1. Atici, F., Eloe, P.: Initial value problems in discrete fractional calculus. Proc. Am. Math. Soc. 137(3), 981–989 (2009)
2. Aydin, M.E.: Effect of local fractional derivatives on Riemann curvature tensor. Ex. Counterex. 5, 100134 (2024)
3. Aydin, M.E., Bektas, M., Ogrenmis, A.O., Yokus, A.: Differential geometry of curves in Euclidean 3-Space with fractional order. Int. Electron. J. Geol. 14(1), 132–144 (2021a)
4. Aydin, M.E., Mihai, A., Yokus, A.: Applications of fractional calculus in equiaffine geometry: plane curves with fractional order. Math. Methods Appl. Sci. 44(17), 13659–13669 (2021b)
5. Büyükkütük, S., Öztürk, G.: Constant ratio curves according to Bishop frame in Euclidean $$3$$-Space. Gen. Math. Notes 28(1), 81–91 (2015)