In this study, 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 reproducing
kernel Hilbert algorithm to construct pointwise numerical solution to
variant forms of fractional sine-Gordon model in fullness of
overdetermination Dirichlet boundary condition. Allocates theoretical
requirements are employed to interpret pointwise numerical solutions to
such fractional models on the space of Sobolev. In addendum, the
convergence of the pointwise numerical algorithm and error estimates are
promoted by global convergence treatises. This handling pointwise
numerical solution depending on the orthogonalization Schmidt process
that can be straightway carried out to generate Fourier expansion within
a fast convergence rate. The soundness and powerfulness of the discussed
algorithm are expounded by testing the solvability of a couple of
time-fractional sine-Gordon models. Some schematic plots and tabulated
results outcomes signalize that the algorithm procedure is accurate and
convenient in the field of fractional sense. Ultimately, future remarks
and concluding are acted with the most focused used references.