Abstract
In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.
Highlights
Fractional calculus is a developing area in many areas of science
Many fractional derivative definitions introduce in the last few centuries
Based on the data in the tables above, we can conclude that the results achieved by the Natural decomposition method are more reliable
Summary
Fractional calculus is a developing area in many areas of science. Scholars are paying attention to fractional differential equations as they are applied to model various implementations such as heat conduction, viscoelasticity, dynamical systems, biology, and so on [1,2,3]. Because of its significance in various fields, numerous methods for studying the computational and exact results of fractional differential equations have been developed. Many fractional derivative definitions introduce in the last few centuries. Riemann–Liouville, Fabrizio, Atangana–Baleanu, Grunwald–Letnikov, and Riesz fractional derivatives are some famous definitions in the literature. The kernel of the Riemann–Liouville and Caputo fractional derivatives is unique. Atangana–Baleanu and Caputo–Fabrizio have recently created two non-singular kernel fractional derivative definitions. Numerous techniques for analyzing fractional differential equations for accuracy and dependability are being investigated
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