Similarity reduction, conservation laws, and explicit solutions for the time-fractional coupled GI equation provided with convergence analysis and numerical simulation

Abstract

In this paper, we consider the time-fractional coupled Gerdjikov-Ivanov (GI) equation within quanta field theory. Primarily, we construct an analytical solution for the considered equation by applying two analyses: Lie group analysis that has been used to detect the infinitesimal generators and similarity reductions for the time-fractional coupled GI. These reductions enable us to reduce the equation under study into a fractional ordinary differential (FOD) form. Then, we implement the power series analysis to solve the reduced equation which is provided by a convergence analysis of the obtained solution. Additionally, we find a numerical solution by the fractional-reduced differential transform (F-RDT) method in the sense of Caputo fractional derivatives accompanied by absolute errors and the effect of the fractional order α. Finally, the conservation laws are derived in the sense of Riemann–Liouville (R-L) fractional derivatives and the new conservation theorem.

Keywords

• Lie group analysis
• Conservation laws
• The time-fractional couple Gerdjikov-Ivanov equation
• Riemann–Liouville derivatives
• Similarity reduction
• Explicit power series