Approximate Solutions of the Coupled M-Truncated Fractional mKdV System Using the Adomian Decomposition Technique

Abstract

This manuscript employs the Adomian decomposition technique (ADT) to develop solutions for the fractional space-time nonlinear mKdV system, incorporating an M-truncated fractional order and supposed initial conditions. The technique yields a power series expansion solution without the need for linearization, weak nonlinear assumptions, or perturbation theory. Software such as Maple or Mathematica was utilized to compute the Adomian formulas for the solution expansion. This technique can also be utilized for a range of nonlinear fractional-order models in mathematical physics. A graphical analysis is provided to demonstrate the behavior of Adomian solutions and how variations in non-integer order values influence the results. The technique is straightforward, clear, and widely applicable to other nonlinear fractional problems in both physics and mathematics. It is believed that these studies significantly advance our understanding of the nonlinear coupled fractional mKdV system and its potential applications in physics and engineering.