Reproducing kernel Hilbert pointwise numerical solvability of fractional Sine-Gordon model in time-dependent variable with Dirichlet condition

In this analysis, the fractional sine-Gordon model in the time-dependent variable domain using Caputo non-integer order basis derivative is presented. The main purpose is to utilize the adaptation of the RKHA to construct PNS to various forms of TFSGM subject to the specific DBC. Several theoretical results are employed to interpret PNSs to such fractional models in the sense of the Hilbert space. The convergence of the RKHA and error estimates are derived to guarantee the PNS outcomes. This handling PNS depending on the bases generated from the Gram Schmidt process and can be immediately carried out to generate the Fourier expansion during a fast convergence order. The soundness and powerfulness of the utilized RKHA are explained by testing the numerical solvability of two TFSGMs. Several geometric plots and tabulated outcomes mentioned that the utilized numerical approach is delicate and accurate in the field of CTFPD. In the end, conclusion and future remarks are given. (paper)