THE FRACTAL MODIFICATION OF THE ROSENAU–BURGERS EQUATION AND ITS FRACTAL VARIATIONAL PRINCIPLE
Peng Xu, F.X. Long, Chun Shan, G. X. Li, Feng Shi, Kang‐Jia Wang
Abstract
A new fractal Rosenau–Burgers equation with He’s fractal derivative is proposed in this work. Exerting the semi-inverse method, two different kinds of the generalized fractal variational principles (GFVPs) of the fractal Rosenau–Burgers equation are constructed. The GFVPs extracted in this paper are expected to bring some new inspiration for the study and application of the variational method in the fractal space.
Topics & Concepts
FractalBurgers' equationMathematicsVariational principleFractal derivativeMathematical analysisFractal dimension on networksStatistical physicsFractal dimensionApplied mathematicsFractal analysisPhysicsPartial differential equationAdvanced Mathematical Theories and ApplicationsFractional Differential Equations SolutionsNonlinear Waves and Solitons