Abstract
In this article, the new iterative transform technique and homotopy perturbation transform method are applied to calculate the fractional-order Cauchy-reaction diffusion equation solution. Yang transformation is mixed with the new iteration method and homotopy perturbation method in these methods. The fractional derivative is considered in the sense of Caputo-Fabrizio operator. The convection-diffusion models arise in physical phenomena in which energy, particles, or other physical properties are transferred within a physical process via two processes: diffusion and convection. Four problems are evaluated to demonstrate, show, and verify the present methods' efficiency. The analytically obtained results by the present method suggest that the method is accurate and simple to implement.