@article {10.3844/ajeassp.2011.133.141, article_type = {journal}, title = {Fractional Quantum Field Theory on Multifractals Sets}, author = {Rami, El-Nabulsi Ahmad}, volume = {4}, number = {1}, year = {2011}, month = {Mar}, pages = {133-141}, doi = {10.3844/ajeassp.2011.133.141}, url = {https://thescipub.com/abstract/ajeassp.2011.133.141}, 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.}, journal = {American Journal of Engineering and Applied Sciences}, publisher = {Science Publications} }