Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations

Mustafa Inc, Abdullahi Yusuf, Aliyu Isa Aliyu and Dumitru Baleanu

Physica A: Statistical Mechanics and its Applications, 2018, vol. 496, issue C, 371-383

Abstract: This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space–time fractional nonlinear evolution equations with Riemann–Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi–Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Keywords: Space–time nonlinear evolution equations; Lie symmetry; RL fractional derivative; Explicit solutions; Cls (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:496:y:2018:i:c:p:371-383

DOI: 10.1016/j.physa.2017.12.119

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