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Neijiang, China

El-Nabulsi R.A.,Neijiang Normal University
Canadian Journal of Physics | Year: 2013

We introduce the notion of a "generalized time-dependent Hubble parameter" for the case of Friedmann-Robertson-Walker cosmology. We obtain a Riccati differential equation for the Hubble parameter, H, and it was observed that the effective equation of state in our framework can cross the phantom divide line as supported by recent astrophysical observations. In addition, the model is able to evolve without initial singularity. © 2013 Published by NRC Research Press. Source


El-Nabulsi R.A.,Neijiang Normal University
Canadian Journal of Physics | Year: 2013

Nonstandard Lagrangians are generating functions of different equations of motion. They have gained increasing importance in many different fields. In fact, nonstandard Lagrangians date back to 1978, when Arnold entitled them "non-natural" in his classic book, Mathematical Methods of Classical Mechanics (Springer, New York. 1978). In applied mathematics, most dynamical equations can be obtained by using generating Lagrangian functions (e.g., power-law and exponential Lagrangians), which has been shown by mathematicians, who have also demonstrated that there is an infinite number of such functions. Besides this interesting field, the topic of fractional calculus of variations has gained growing importance because of its wide application in different fields of science. In this paper, we generalize the fractional actionlike variational approach for the case of a nonstandard exponential Lagrangian. To appreciate this new approach, we explore some of its main consequences in Einstein's general relativity. Some results are revealed and discussed accordingly mainly the transition from general relativity to complex relativity and emergence of a discrete gravitational coupling constant. © 2013 Published by NRC Research Press. Source


El-Nabulsi A.R.,Neijiang Normal University
Indian Journal of Physics | Year: 2013

This work discusses some developments in classical gauge field theory which have grown out of the ideas of non-standard Lagrangians in the framework of the calculus of variations. A substantial part of this work is concerned with the modification of some basic equations of classical field theories starting from a power-law Lagrangian functional with time-dependent power and which belongs to the class of non-standard Lagrangians. Many equations principally the modified Proca equation and some modified dispersion relations for the consequent field equations are derived. © 2013 Indian Association for the Cultivation of Science. Source


El-Nabulsi A.R.,Neijiang Normal University
Indian Journal of Physics | Year: 2013

In this paper we set up a fractional generalization of Einstein's field equations based on fractional derivatives inside the geodesic action integral and obtained non-local fractional Einstein's field equations. More specifically, the total derivative of any generalized coordinate is considered to take the special form D = Dclassical + kDfractional,k is a real parameter, Dclassical is the classical derivative operator and D fractional is the modified left Riemann-Liouville fractional derivative operator so that the classical result of the calculus of variations is considered as a particular case. Many attractive astrophysical and cosmological solutions have been obtained and discussed in some details. © 2012 Indian Association for the Cultivation of Science. Source


El-Nabulsi R.A.,Neijiang Normal University
Nonlinear Dynamics | Year: 2013

Two mathematical physics' approaches have recently gained increasing importance both in mathematical and in physical theories: (i) the fractional action-like variational approach which founds its significance in dissipative and non-conservative systems and (ii) the theory of non-standard Lagrangians which exist in some group of dissipative dynamical systems and are entitled "non-natural" by Arnold. Both approaches are discussed independently in the literature; nevertheless, we believe that the combination of both theories will help identifying more hidden solutions in certain classes of dynamical systems. Accordingly, we generalize the fractional action-like variational approach for the case of non-standard power-law Lagrangians of the form L1+γ (γ∈ℝ}) recently introduced by the author (Qual. Theory Dyn. Syst. doi: 10.1007/s12346-012-0074-0, 2012). Many interesting features are discussed in some details. © 2013 Springer Science+Business Media Dordrecht. Source

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