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In this paper, we propose a new technique for solving conformable Cauchy reaction-diffusion equations (CRFEs). These equations are widely used as models for spatial effects in engineering, biology and ecology sciences. The conformable derivatives are considered in Khalil sense. This method is based on perturbation theory and the conformable Laplace transformation (CLHPM). The solutions presented in this work can be used to obtain the closed form of the solutions if they are needed. The outcomes display that new technique is of high validity, more convenient and effective to use. The results presented in this paper show that the CLHPM is a powerful mathematical tool for solving other nonlinear conformable equations.