An Effective New Iterative Method to Solve Conformable Cauchy Reaction-Diffusion Equation via the Shehu Transform

Abstract

For the first time, we establish a new procedure by using the conformable Shehu transform (CST) and an iteration method for solving fractional-order Cauchy reaction-diffusion equations (CRDEs) in the sense of conformable derivative (CD). We call this recommended method the conformable Shehu transform iterative method (CSTIM). To evaluate the efficacy and consistency of CSTIM for conformable partial differential equations (PDEs), the absolute errors of four CRDEs are reviewed graphically and numerically. Furthermore, graphical significances are correspondingly predicted for several values of fractional-order derivatives. The results and examples establish that our new method is unpretentious, accurate, valid, and capable. CSTIM does not necessarily use He’s polynomials and Adomian polynomials when solving nonlinear problems, so it has a strong advantage over the homotopy analysis and Adomian decomposition methods. The convergence and absolute error analysis of the series solutions is also offered.