The Lorentz transformations and one observation in the perspective of fractional calculus

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Daniel Cao Labora (Author) Other; António M. Lopes (Author) FEUP; J. A. Tenreiro Machado (Author) Other

Journal

Title: Communications in Nonlinear Science and Numerical Simulation

Vol. 78

Pages: 1-14

ISSN: 1007-5704

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 1 Citation

Other information

Authenticus ID: P-00Q-NKE

DOI: 10.1016/j.cnsns.2019.104855

Abstract (EN): The Lorentz transformations are a key element in the Special Relativity Theory. Their deduction is a consequence of three physical principles, namely, relativity, homogeneity and isotropy, although this issue is commonly omitted. In the first part of the paper, we provide a rigorous mathematical deduction for the formula of Lorentz transformations, including a generalization for accelerated frames. In a second part, we establish a relationship between the formulations in the perspective of integer and Fractional Calculus. We examine when a magnitude (measured as an integral from the point of view of one observer) can be computed as a fractional integral from the point of view of the other observer. Finally, we compute the velocity in a relativistic travel from the solution of a given fractional integral equation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14