An analytical study of reaction diffusion, (3 + 1)-dimensional diffusion equations using Caputo Fabrizio fractional differential operator

Abstract

Motivated by the memory features and property to portray substance heterogeneities and arrangement with various sizes of Caputo Fabrizio operator of fractional order to investigate hidden dynamics of several nonlinear differential systems. In the present work, we conduct analytical study and obtain numerical simulations of one, two and (3+1)-dimensional Caputo-Fabrizio reaction-diffusion equations. Hybrid Laplace transform-based iterative method is constructed to find approximate solutions of diffusion equations involving Caputo–Fabrizio derivative with the exponential kernel. We have also carried out comparative analysis between Caputo and Caputo Fabrizio fractional differential operator. Moreover, we have obtained absolute error between exact and approximate solutions. 2D and 3D plots are obtained to demonstrate the efficiency of method graphically.