A Scaling Method and its Applications to Problems in Fractional Dimensional Space

Authors

Sami I. Muslih, Southern Illinois University Carbondale
Om P. Agrawal, Southern Illinois University Carbondale

Comments

© 2009 American Institute of Physics

Published in Journal of Mathematical Physics, Vol. 50 No. 12 (2009) at doi: 10.1063/1.3263940

Abstract

A scaling method is proposed to find (1) the volume and the surface area of a generalized hypersphere in a fractional dimensional space and (2) the solid angle at a point for the same space. It is demonstrated that the total dimension of the fractional space can be obtained by summing the dimension of the fractional line element along each axis. The regularization condition is defined for functions depending on more than one variable. This condition is applied (1) to find a closed form expression for the fractional Gaussian integral, (2) to establish a relationship between a fractional dimensional space and a fractional integral, (3) to develop the Bochner theorem, and (4) to obtain an expression for the fractional integral of the Mittag–Leffler function. Some possible extensions of this work are also discussed.

Recommended Citation

Muslih, Sami I. and Agrawal, Om P. "A Scaling Method and its Applications to Problems in Fractional Dimensional Space." Journal of Mathematical Physics 50, No. 12 (Dec 2009). doi:10.1063/1.3263940.