Pell–Lucas Collocation Method for Time-Fractional Partial Integro-Differential Equations

This paper presents a Pell–Lucas collocation method for time-fractional partial integro-differential equations (TFPIDEs) with initial and boundary conditions, where the fractional derivative is taken in the Caputo sense. The unknown solution is approximated by a truncated bivariate Pell–Lucas series, and the governing equation together with the initial and boundary conditions is discretized at uniform collocation points. Operational matrices are employed to represent the fractional-time derivative, spatial derivatives, and Volterra integral term, thereby reducing the continuous problem to a system of algebraic equations. An upper error bound in the infinity norm and a residual-based error-estimation procedure are also discussed. Numerical examples illustrate the applicability and accuracy of the proposed approach and include comparisons with exact solutions and with results reported in the literature for alternative methods.