An Insight on the (2 + 1)-Dimensional Fractal Nonlinear Boiti–leon–manna–pempinelli Equations

Abstract

With the aid of a new fractal derivative, the nonlinear Boiti–Leon–Manna–Pempinelli equation (NBLMPE) with nonsmooth boundary is explored. The variational principle of the fractal NBLMPE is successfully established by fractal wave transformation (FWT) and fractal semi-inverse method (SIM) and strong minimum condition of fractal NBLMPE is proven with the fractal Weierstrass theorem. Based on the two-scale transformation method (TSTM) and homogeneous equilibrium method (HBM), soliton-like solutions for the [Formula: see text]-dimensional (SLS [Formula: see text]D) fractal NBLMPE are acquired. A powerful means of coupling HBM and TSTM to solve fractal differential equations is proposed.

Adapting Laplace residual power series approach to the Caudrey Dodd Gibbon equation

“…Calculus is one of the branches of great importance, especially differential equations of various types, whether ordinary or partial. Fractional differential equations have recently emerged in many applications such as plasma physics, image processing, laser optics, biomedical engineering, viscoelasticity, hydrology, signal processing and control system 1 – 13 . Some of these equations do not have an analytical solution, so we resort to approximate solutions using distinct analytical methods such as: the adomain decomposition method 14 , the variational iteration method 15 , the homotopy method 16 – 18 , and the Gegenbauer wavelet method 19 .…”