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

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. (C) 2019 Elsevier B.V. All rights reserved.