Pointwise numerical simulation of one-dimensional fractional sine-Gordon model in time-dependent variable using reproducing kernel Hilbert algorithm

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.