A novel analysis of the fractional Cauchy reaction-diffusion equations

Abstract

This article considers the Cauchy reaction-diffusion equations and derives the numerical solutions using the fractional natural decomposition method (FNDM). The projected solution approach works without conversion or perturbation. The examples confirm the method’s accuracy and reliability, allowing for fractional order studies in real-world problems. Plots and tables validate the accuracy of the proposed scheme. This research reveals the influences of temporal history in the fractional Cauchy reaction-diffusion equations, which is the novelty of this work. © 2025 Elsevier B.V., All rights reserved.