Fractional illusion theory of space: Fractional gravitational field with fractional extra-dimensions

Rami, El-Nabulsi Ahmad

doi:10.1016/j.chaos.2008.12.008

Cited by 10 publications

(1 citation statement)

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“…Many encouraging results were successfully obtained and discussed (El-Nabulsi and Torres, 2008;El-Nabulsi, 2007;2008b;2008c;2009b;2009c;2009d;2009e;2009f;2009g). In order to stimulate more interest in the subject and to show its utility, this contribution is devoted to a new generalization of the FALVA by introducing mainly inside the fractional action-like integral the Saxena-Kumbhat hypergeometric fractional operator, augmented by a fractional derivative and a dynamical fractional exponent defined on multifractal time and space sets, in particular when the fractional dimensions of time and space are dynamical, e.g., i…”

Section: Introductionmentioning

confidence: 99%

Fractional Quantum Field Theory on Multifractals Sets

Rami¹

2011

American Journal of Engineering and Applied Sciences

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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.

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