Study of radioactive decay process of uranium atoms via fractals-fractional analysis
Kamal Shah, Thabet Abdeljawad
Abstract
This manuscript is devoted to derive a mathematical formulation for radioactivity process of uranium to radium which decays to produce radon. Radon which further decays to produce polonium atoms. The said interesting phenomenon is investigated using the concept of fractals-fractional calculus. The concerned differential operator plays significant role to describe the complex and irregular geometry of real world problems. Also, we deduce the existence theory of such process through mathematical analysis using fractal type Laplace transform. Finally, a computational algorithm is established to simulate the corresponding results for various fractals and fractional orders. In this regard, computational software Matlab-16 is used to simulate our theoretical results. Various graphical presentations are displayed for the computed theoretical results. A comparison with classical traditional order model has also done.