Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel

Abstract This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up new Hilbert space that satisfies initial and boundary conditions. collocation applied obtain precise numerical approximation using basis functions based on shifted first-kind Chebyshev polynomials (SCP1K). Furthermore, we support our study by careful error analysis suggested expansion. results show very accurate effective.