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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 789769, 5 pages
http://dx.doi.org/10.1155/2014/789769
Research Article

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

1MaSIM Focus Area, North-West University, Mafikeng 2735, South Africa
2Department of Mathematical Sciences, University of South Africa, Florida 1709, South Africa

Received 27 May 2014; Revised 21 June 2014; Accepted 22 June 2014; Published 8 July 2014

Academic Editor: Abdon Atangana

Copyright © 2014 S. C. Oukouomi Noutchie and E. F. Doungmo Goufo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.