Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method

Abstract

In quantum field theory, the fractional Kundu-Eckhaus and massive Thirring models are nonlinear partial differential equations under fractional sense inside nonlinear Schrödinger class. In this study, approximate analytical solutions of such complex nonlinear fractional models are acquired by means of conformable residual power series method. This method presents a systematic procedure for constructing a set of periodic wave series solutions based on the generalization of conformable power series and gives the unknown coefficients in a simple pattern. By plotting the solutions behavior of the models; the convergence regions in which the solutions coincide to each other are checked for various fractional values. The approximate solutions generated by the proposed approach are compared with the exact solutions -if exist- and the approximate solutions obtained using qHATM and LADM. Numerical results show that the proposed method is easy to implement and very computationally attractive in solving several complex nonlinear fractional systems that occur in applied physics under a compatible fractional sense.