Lie Symmetry Analysis, Conservation Laws, Power Series Solutions, and Convergence Analysis of Time Fractional Generalized Drinfeld-Sokolov Systems

Abstract

In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fractional differential operator, the time fractional GDSS equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. Moreover, we have constructed conservation laws for time fractional GDSS and obtained explicit power series solutions of the reduced nonlinear ODEs that converge. Lastly, some figures are presented for explicit solutions.

Invariant analysis, approximate solutions, and conservation laws for the time fractional higher order Boussinesq–Burgers system

“…By using the power series method [19,20,39,40], we intend to construct analytic approximate solutions of the time fractional higher order B-B system.…”

Conservation Laws and Explicit Solution of system of Fractional-Order Coupled Nonlinear Hirota Equations by Lie Symmetry Analysis

“…Noether's theorem [27,31,33] established a relation between conservation laws and symmetry of differential equations and applied on FPDEs without Lagrangian operators. Recently, authors [34,[36][37][38][39]47] provided invariance structure, explicit exactsolutions with power series solution and conservation analysis of Boussinesq-Burger's system, Drinfeld-Sokolov-Satsuma-Hirota coupled KdV and m-KdV equations via Lie symmetry analysis. Biswas et al [12][13][14] have worked on dual dispersion, power laws, conservation laws and optimal quasi-solitons by Lie symmetry analysis.…”

Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws

“…Noether's theorem for symmetries was proposed by Cicogna et al [30], while Ibragimov [31] studied the applicability of the conservation theory in linear and nonlinear classical models. Invariance structure, explicit precise solutions with a power series solution, and a conservation analysis of the Boussinesq system, Burger's coupled KdV and m-KdV equations, and Drinfeld-Sokolov-Satsuma-Hirota equations are explored in [32][33][34][35][36][37]. Biswas et al [38][39][40] worked on dual dispersion, power laws, conservation laws and optimal quasi-solitons using Lie symmetry analysis.…”