Hermite Cubic Spline Collocation Method for Nonlinear Fractional Differential Equations with Variable-Order

In this paper, we develop a Hermite cubic spline collocation method (HCSCM) for solving variable-order nonlinear fractional differential equations, which apply C1-continuous nodal basis functions to an approximate problem. We also verify that the order of convergence HCSCM is about O(hmin{4−α,p}) while interpolating function belongs Cp(p≥1), where h mesh size and α derivative. Many numerical tests are performed confirm effectiveness include Helmholtz equations Burgers equation constant-order with Riemann-Liouville, Caputo Patie-Simon sense as well two-sided cases.