NEW APPLICATIONS OF THE FRACTIONAL DERIVATIVES TO EXTRACT ABUNDANT SOLITON SOLUTIONS OF THE FRACTIONAL ESTEVEZ–MANSFIELD–CLARKSON EQUATION IN MATHEMATICAL PHYSICS

The Estevez–Mansfield–Clarkson (EMC) equation arises in the description of the development of patterns in liquid drops. This work presents a comparative study of the nonlinear space-time fractional EMC equation for the M-truncated derivative and a newly proposed local fractional derivative. The modified auxiliary equation technique and the modified simple equation technique are employed to retrieve the exact wave solutions of the space-time fractional EMC equation. As a result, a variety of soliton patterns are obtained for suitably assigned parametric values. The fractional effects for the two kinds of fractional differential operators are demonstrated using graphical simulations for some of the obtained solutions. The evolution of the soliton with increasing value of the fractional order for both kinds of fractional derivatives is also demonstrated. Three-dimensional graphs, 2D comparison plots and density plots are included to understand the dynamical behavior of the governing equation. The reported solutions may be useful in industry and innovation as well as in the exploration of more fractional order nonlinear models arising in mathematical physics.