A New Perspective on the Exact Solutions of the Local Fractional Modified Benjamin–Bona–Mahony Equation on Cantor Sets

A new local fractional modified Benjamin–Bona–Mahony equation is proposed within the derivative in this study for first time. By defining some elementary functions via Mittag–Leffler function (MLF) on Cantor sets (CSs), a set of nonlinear ordinary differential equations (NLFODEs) constructed. Then, fast algorithm namely Yang’s special method employed to find non-differentiable (ND) exact solutions. method, we can extract abundant solutions just one step. Finally, obtained CS are outlined form 3-D plot. The whole calculation process clearly shows that simple and effective, be applied investigate ND other PDEs.