Exact solutions and non-linear adaptive boundary control problem of the fractional modified generalized KdV-burgers equation

This article extends a modified generalized KdV-Burgers equation to the conformable fractional version with the aim of exploring novel solution structures and non-linear adaptive boundary control problems for fractional-order models. The results obtained include hyperbolic functional solutions of the fractional modified generalized KdV-Burgers equation and a non-linear adaptive boundary control law designed by attaching initial and boundary value conditions. It is demonstrated that the obtained hyperbolic functional solutions exhibit novel spatial structures, and that the solution of the fractional initial and boundary value problem is globally exponential stability.