We present a compilation of work dedicated to the progress of a physical interpretation of fractional derivative operators and especially to a fractional extension of group theory and its application to physical problems. Within the framework of fractional calculus new concepts and strategies emerge, which make it possible, to obtain new challenging insights and surprising correlations between different branches of physics.

The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory andÂ surprises with new intriguing insights.

Just have a look in the *Books* section for introductory literature on fractional calculus. In the *Publications* sections we have listed references to articles in inverse chronological order.

*FREE ACCESS:* Most results of our research are accessible via arXiv.org.

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**Solutions of the fractional SchrĂ¶dinger equation via diagonalization –**

A plea for the harmonic oscillator basis

part 1: the one dimensional case

A plea for the harmonic oscillator basis

part 1: the one dimensional case

**reference: **arXiv:1805.03019