An Implicit Difference Scheme for the Fourth-Order Nonlinear Evolution Equation with Multi-Term Riemann–Liouvile Fractional Integral Kernels

In this paper, an implicit difference scheme is proposed and analyzed for a class of nonlinear fourth-order equations with the multi-term Riemann–Liouvile (R–L) fractional integral kernels. For convection term, we handle implicitly attain system algebraic by using Galerkin method based on piecewise linear test functions. The terms are treated convolution quadrature. order to obtain fully discrete method, standard central approximation used discretize spatial derivative. stability convergence rigorously proved energy method. addition, existence uniqueness numerical solutions systems strictly. Additionally, introduce compare Besse relaxation algorithm, Newton iterative linearized algorithm solving systems. Numerical results confirm theoretical analysis show effectiveness