"Newly Proposed Solutions Using Caputo, Caputo– Fabrizio and Atangana

Progress in Fractional Differentiation & Applications

Article Title

Newly Proposed Solutions Using Caputo, Caputo– Fabrizio and Atangana–Baleanu Fractional Derivatives: A Comparison

Authors

Anas A. M. Arafa, Department of Mathematics, College of Sciences and Arts, Methnab, Qassim University, P.O. Box 931, Buridah, 51931, Methnab, Kingdom of Saudi Arabia\\ Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt Follow

Author Country (or Countries)

Egypt

Abstract

The aim of this paper is to demonstrate the extent to which the new iterative Sumudu transform method (NISTM) helps in solving three fractional KdV–Burgers equations (KdVB). In fact, new explanatory solutions are being obtained by using Caputo sense, which represents kernels power law type, Caputo–Fabrizio (CF) standing for exponentially with decaying type kernel and the Atangana–Baleanu (AB) representing the Mittag-Leffler type kernel. It is found that the model consisting of ABC fractional derivatives are affected more by the past than Caputo fractional derivative and CF fractional derivative. The accuracy and efficiency of the NISTM has been shown by studying the convergence of this technique.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080203

Recommended Citation

A. M. Arafa, Anas (2022) "Newly Proposed Solutions Using Caputo, Caputo– Fabrizio and Atangana–Baleanu Fractional Derivatives: A Comparison," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 2, Article 3.
DOI: http://dx.doi.org/10.18576/pfda/080203
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss2/3

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