Revised residual power series method in Laplacian space for space‐time fractional PDEs with proportional delayed arguments

Abstract

This paper developed a new hybrid residual power series (RPS) method in the space of Laplace transform (in brief, ) for the study of the nonlinear space‐time fractional model of partial differential equations with proportional delayed arguments (STF‐PDEDAs). The main objective of this technique is to convert the target nonlinear STF‐PDEDAs into the algebraic equation in the space. The newly transformed equation is solved by utilizing the revised RPS method to achieve series approximations, and refer to this technique as RPSM. Different kinds of attractive applications of STF‐PDEDAs are discussed utilizing proposed RPSM to reveal its efficiency, effectiveness, and adaptability for constructing series solutions to the referred STF‐PDEDAs. The numerical experiments and graphical findings have been computed for different fractional parameter values to analyze the behavior of RPSM solutions and to test the authenticity and applicability of the present method in comparison to other existing results obtained by some rigorous techniques. The outcomes conclude that proposed RPSM is easy to understand and straightforward to provide results converging to its exact solution.