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.
Copyright © 2020 Dnyanoba B. Dhaigude, Vidya N. Bhadgaonkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. B. Dhaigude, V. N. Bhadgaonkar, An analytical study of reaction diffusion, (3 + 1)-dimensional diffusion equations using Caputo Fabrizio fractional differential operator, J. Math. Comput. Sci. 11 (2021), 183–202. https://doi.org/10.28919/jmcs/5084
BibTeX
@article{Dhaigude2021,
author = {Dhaigude, Dnyanoba B. and Bhadgaonkar, Vidya N.},
title = {An analytical study of reaction diffusion, (3 + 1)-dimensional diffusion equations using Caputo Fabrizio fractional differential operator},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {183--202},
doi = {10.28919/jmcs/5084}
}