An advanced method with convergence analysis for solving space-time fractional partial differential equations with multi delays

This study considers the space-time fractional partial differential equations with multi delays under a unique formulation, proposing a numerical method involving advanced matrix system. This matrix system is made up of the matching polynomial of complete graph together with fractional Caputo and Jumarie derivative types. Also, the derivative types are scrutinized to determine which of them is more proper for the method. Convergence analysis of the method is established via an average value of residual function using double integrals. The obtained solutions are improved with the aid of a residual error estimation. A general computer program module, which contains few steps, is developed. Tables and figures prove the efficiency and simplicity of the method. Eventually, an algorithm is given to illustrate the basis of the method.