American Journal of Engineering and Applied Sciences

Fractional Quantum Field Theory on Multifractals Sets

El-Nabulsi Ahmad Rami

DOI : 10.3844/ajeassp.2011.133.141

American Journal of Engineering and Applied Sciences

Volume 4, Issue 1

Pages 133-141

Abstract

Problem statement: This study is a contribution to the general program of describing complex dynamical systems using the tool of fractional calculus of variations. Approach: Following our previous work, fractional quantum field theory based on the fractional actionlike variational approach supported by Saxena-Kumbhat fractional integrals functionals, fractional derivative of order (α, β) and dynamical fractional exponent on multi-fractal sets is considered. Results: In order to build the required theory, we introduce the Saxena-Kumbhat hypergeometric fractional functionals determined on the functions on a multifractal sets. We prove, developing the corresponding fractional calculus of variations, that a hierarchy of differential equations can be developed from the extended fractional Lagrangian formalism. Besides, a generalization of the resulting Hamiltonian and Lagrangian dynamics on the complex plane is addressed. Conclusion: The new complexified dynamics guides to a new dynamics which may differ totally from the classical mechanics cardinally and may bring new appealing consequences. Some additional interesting results are explored and discussed in some details.

Copyright

© 2011 El-Nabulsi Ahmad Rami. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.