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Turkish Journal of Physics

DOI

10.3906/fiz-1705-11

Abstract

$F^\alpha$-calculus was recently presented for fractals. We show that the $F^\alpha$-derivative satisfies the chain rule and affirms that the dimension of a quantum mechanical path is two. $F^\alpha$-calculus allows us to extend quantum mechanics to fractal curves. To show the applicability of $F^\alpha$-calculus, we study the fractal model of a particle in a box. $F^\alpha$-calculus is suitable for describing the motion of particles with a fractal route through matter. In addition, we extend Landau's energy straggling method of charged particles to fractals.

First Page

104

Last Page

115

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