LAUSR

Abstract This study aims to efficiently solve the space-time fractional partial integro-differential equations with spatial-time delays, employing a fast numerical methodology dependent upon the matching polynomial of complete graph and matrix-collocation procedure. This methodology provides a sustainable approach for each computation limit since it arises from the durable graph structure of complete graph and fractional matrix relations. The convergence analysis is established using the residual function of mean value theorem for double integrals. An error estimation is also implemented. All computations are performed with the aid of a unique computer program, which returns the desired results in seconds. Some specific numerical problems are tested to discuss the applicability of the method in tables and figures. It is stated that the method stands for fast, simple and highly accurate computation.