Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 25, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X17400060
Keywords
Exact Traveling-Wave Solution; Local Fractional Boussinesq Equation; Local Fractional Derivative; Fractals
Funding
- State Key Research Development Program of the People's Republic of China [2016YFC0600705]
- Natural Science Foundation of China [51323004]
- Priority Academic Program Development of Jiangsu Higher Education Institutions [PAPD2014]
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The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.
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