A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.