Space-Time Fractional KdV–Burger–Kuramato Equation with Time Dependent Variable Coefficients: Lie Symmetry, Explicit Power Series Solution, Convergence Analysis and Conservation Laws

• Published in: International journal of applied and computational mathematics Vol. 8; no. 2
• Main Authors: Yadav, Vikash, Gupta, Rajesh Kumar
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.04.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied mathematics; Computational mathematics; Computational Science and Engineering; Conservation laws; Convergence; Dependent variables; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Nuclear Energy; Operations Research/Decision Theory; Operators (mathematics); Ordinary differential equations; Original Paper; Partial differential equations; Power series; Spacetime; Symmetry; Theoretical; Time dependence; Conservation laws; Riemann–Liouville fractional differential operator; Power series solution; 70H33; Erdélyi–Kober fractional differential operator; 76M60; 35R11; Symmetry analysis; KdV–Burger–Kuramato equation
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-021-01229-6

In this paper, Lie symmetry reduction, power series solutions, convergence analysis and conservation laws have been examined for the space-time fractional KdV–Burger–Kuramato equation with time dependent variable coefficients. The obtained symmetries and the Erdélyi–Kober fractional differential operator have been used to reduce the original nonlinear partial differential equation into a nonlinear ordinary differential equation. The power series solutions are also derived for the equation under consideration. Further, the obtained power series solution are examined for the convergence. The generalized Noether method has been utilized to investigate the conservation laws of the equation.