We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler–DeWitt equation of second order, showing that a Bohm–de Broglie interpretation can be constructed. That combination of fractional quantization and Bohmian interpretation provides us a new quantization method, in which the quantum potential is the criterion to say if a quantum solution is acceptable or not to be further studied. We show that a wide range of solutions for the scale factor is possible. Among all of those, a bouncing solution analogous to the perfect fluid cosmology seems to deserve special attention.

中文翻译：

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具有相称分数导数的Fab Four John理论的量子宇宙学

我们研究了通过非最小导数耦合宇宙论的分数导数进行的量化，即Fab Four John理论。其哈密顿量表示了瞬时矩中的分数幂问题。该问题在此通过应用所谓的适形分数导数来解决。这导致了Wheeler-DeWitt方程为二阶，表明可以构造Bohm-de Broglie解释。分数量化和Bohmian解释的结合为我们提供了一种新的量化方法，其中以量子势为标准来说明量子解决方案是否可接受或是否有待进一步研究。我们证明了比例因子的广泛解决方案是可能的。在所有这些当中，