Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 29, Issue 3, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X21500596
Keywords
Fractal Derivative; Fractal Burgers– BBM Equation; Two-scale Transform Method; Variational Principle; Fractal Variational Iteration Transform Method
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This paper describes the Burgers-Benjamin-Bona-Mahony (Burgers-BBM) equation using fractal derivative, establishing its variational principle and proposing a new approximate method called Fractal Variational Iteration Transform Method (FVITM). The example shows FVITM to be an excellent tool for studying fractal models.
In this paper, the Burgers-Benjamin-Bona-Mahony (Burgers-BBM) equation is described according to the use of the fractal derivative. The variational principle of the fractal Burgers-BBM equation is successfully established by adopting the fractal semi-inverse method, which is very helpful to research the structures of fractal solution for the solitary waves and construct the conservation law. Based on the proposed variational theory, a novel approximate method is successfully proposed for the fractal Burgers-BBM equation, which is called Fractal Variational Iteration Transform Method (FVITM). The example illustrates the FVITM is an excellent and fascinating tool for fractal models.
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