Construction of the New Wave Solutions of Modified Camassa-Holm and Degasperis-Procesi Equations with Atangana’s Conformable Derivative

İngilizce (OpenAlex)

In this study it is aimed to expose the new exact wave solutions of time-fractional modified Camassa-Holm (mCH) and time-fractional modified Degasperis-Procesi (mDP) equations due to being extensively used to delineate many physical phenomena in fluid mechanics, hydrodynamics and optical fibers. The aforementioned fractional equations are transformed into nonlinear ordinary differential equations (NLODE) considering the Atangana’s conformable derivative (ACD). Then the (m+1/G’)-expansion method is applied for these NLODEs to obtain the desired exact solutions of the fractional evolution equations. The evaluations are fulfilled through the software system Mathematica. Also the reported solutions in this manuscript are compared with the ones in the literature for the time-fractional CH and DP equations and the behaviors of the solutions are presented graphically.