Abstract
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.
Highlights
The theory of the local fractional derivative (LFD) is a mathematical tool for describing fractals, that was used to model the fractal complexity in shallow water surfaces,[14] LC-electric circuit,[15] traveling-wave solution of the Burgerstype equation,[16] PDEs,[17,18,19,20] ODEs,[21] and inequalities.[22,23]
Taking α2 = 0, we obtain from Eq (46) that dδ Θδ (ψ) dψδ Fractals 2017.25
The non-differentiable-type traveling-wave transform is used to generalize the problem to the nonlinear local fractional ODE
Summary
Fractional-order derivatives (FDs) have successfully been applied for describing fractal problems in engineering.[1,2,3,4,5,6,7,8] Recent examples are the heat transport in fractal media,[9] fractal hydrodynamic equations,[10] fractal electrostatics,[11] fractal Fokker– Planck equations[12] and fractal description of stress and strain in elasticity.[13]. The main aim of the paper is to derive the Boussinesq-type model in fractal domain and to find the exact nondifferentiable-type traveling-wave solution for the two-dimensional problem. 4 and 5, the traveling-wave transform and the exact solutions are discussed, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
