Fractional differential equations and the Schrödinger equation

摘要

In a previous paper, we defined, following a previous work of Kolvankar and Gangal, a notion of α-derivative, 0<α<1. In this article, we study α-differential equations associated to our fractional calculus. We then discuss a fundamental problem concerning the Schrödinger equation in the framework of Nottale's scale relativity theory.