Fractional Quantum Field Theory on Multifractals Sets | Science Publications

American Journal of Engineering and Applied Sciences

El-Nabulsi A. Rami¹ 

关键词: Fractional action-like variational approach;    multifractal sets;    Euler-Lagrange equations;    Saxena-Kumbhat fractional integral;    fractional derivative;    dynamical fractional exponent;   

DOI  :  10.3844/ajeassp.2011.133.141

学科分类：工程和技术（综合）

来源: Science Publications

【 摘 要 】

Problem statement: This study is a contribution to the general program of describingcomplex dynamical systems using the tool of fractional calculus of variations. Approach: Followingour previous work, fractional quantum field theory based on the fractional actionlike variationalapproach 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 buildthe required theory, we introduce the Saxena-Kumbhat hypergeometric fractional functionals determinedon the functions on a multifractal sets. We prove, developing the corresponding fractional calculus ofvariations, that a hierarchy of differential equations can be developed from the extended fractionalLagrangian formalism. Besides, a generalization of the resulting Hamiltonian and Lagrangian dynamicson the complex plane is addressed. Conclusion: The new complexified dynamics guides to a newdynamics which may differ totally from the classical mechanics cardinally and may bring new appealingconsequences. Some additional interesting results are explored and discussed in some details.

【 授权许可】

Unknown