Fractional Gravity/Cosmology in Classical and Quantum Regimes, Second Edition

Dear Colleagues,

In fractional calculus, the power of the differentiation operator (which is not local) is any rational (or even real or complex) number. Recently, it has been widely used in various branches of physics. Such frameworks have played an important role in understanding complex systems in both the classical and quantum regimes. In what follows, we will focus on fractional gravity and cosmology.

Regarding the classical regime, fractional derivative cosmology has been established by two different methods: (i) The Last Step Modification method is the simplest one, in which the given cosmological field equations for a specific model are replaced by the corresponding fractional field equations. (ii) The First Step Modification method can be considered a more fundamental methodology. In this method, one starts by establishing fractional derivative geometry. More concretely, the variational principle for fractional action is applied to establish a modified cosmological model.

The main objective of the mentioned methods is the investigation of open problems in gravity/cosmology.  

In the context of fractional quantum mechanics, the fractional Schrödinger equation (SE) has been obtained with space, time, and spacetime fractional derivatives. These frameworks have been applied to solve various problems with different potentials.

Moreover, fractional quantum mechanics has been applied as a tool within quantum field theory and gravity for fractional spacetime.

Inspired by the modified SE mentioned above, the fractional Wheeler–DeWitt equation associated with fractional quantum cosmology was also set up.

We welcome new ideas, current developments, future perspectives, and review articles on the above fractional proposals relevant to gravitation and cosmology, which are the focus of this Special Issue.

Dr. Seyed Meraj Mousavi Rasouli
Dr. Shahram Jalalzadeh
Guest Editors

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• fractional calculus
• fractional derivatives
• riesz fractional operator
• caputo fractional operator
• fractional Brownian motion
• levy path integrals
• fractional-action-like variational approach
• fractional quantum mechanics
• fractional classical cosmology
• fractional quantum cosmology
• non-local operators

• Fractional Gravity/Cosmology in Classical and Quantum Regimes in Fractal and Fractional (4 articles)