Numerical Evaluation of Fractional-Order Forced Duffing Equation with Non-Classical Boundary Conditions via Reproducing Kernel Hilbert Method

In this work, we aim to propose a reliable numerical scheme for the numerical investigation of solutions to the fractional forced Duffing equation with non-classical boundary conditions. The solution methodology in this scheme is mainly founded on the reproducing kernel theory, whereby an orthonormal basis is generated from the reproducing kernel functions which correspond to the non-classical constraint conditions of the proposed equation, to finally formulate the solution in the form of a uniformly convergent expansion series on the desired reproducing Hilbert space. Convergence analysis is obtained in a preferred reproducing Hilbert space. Finally, to ensure the structural integrity and reliability of the offered algorithm, we scrutinize the approximate solutions to a meaningful numerical example.