Reduction of beta-ray intensity with respect to thickness of absorber material exhibits a non-exponential behavior due to the different types of the energy loss processes and many different fractal-like paths followed by beta particles in material. According to Caputo formalism of fractional calculus, the reduction process of beta-ray intensity is governed by using a simple fractional differential equation of order alpha approximate to 0.31. The solution is obtained in terms of Mittag-Leffler function which depends on a mass attenuation coefficient mu(m) and a fractional order a that can be considered as a measure of fractality of absorbing material. In the experimental part of the study, Tc-99, Cl-36, C-14, (210)pb and Pm-147 a Pm radioisotopes have been used as beta sources. In the framework of fractional calculus approach, the experimental and calculated half-value thicknesses of all samples have been obtained in agreement with each other. (C) 2014 Elsevier B.V. All rights reserved.