Numerical solution of multi-fractional order initial-boundary value problems based on Chebyshev-reproducing kernel method

<span style="color: rgb(51, 51, 51); font-family: &quot;Open Sans&quot;, sans-serif; font-size: 17.6px;">In this paper, an iterative approach using the Chebyshev-reproducing kernel method is proposed for the numerical solution of multi-fractional order initial-boundary value problems. This method is based on the reproducing kernel Hilbert space technique, which requires a linear operator and provides approximate solutions utilizing the reproducing kernel function. This reproducing kernel function is obtained by shifted Chebyshev polynomials to develop a more comprehensive approach. Moreover, additional basis functions are introduced for the initial boundary conditions of the considered problem, effectively eliminating the difficulties in homogenizing these conditions. The proposed approach is evaluated on linear and nonlinear multi-fractional order initial-boundary problems with tables and graphs showing the comparison of obtained results.</span>