Abstract
In this paper, the Lie symmetry analysis method is applied to the space-time fractional cubic Schrödinger equation. The group generators are obtained for the system of space-time fractional differential equations. They are utilized to reduce the system of fractional partial differential equations with Riemann–Liouville fractional derivative to the system of fractional ordinary differential equations with Erdélyi–Kober fractional derivative. Then, the power series method is applied to derive explicit solutions for the reduced systems. Furthermore, the traveling wave solutions of the integer-order cubic Schrödinger equation is obtained.
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