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Open AccessArticle

Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators

1
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
2
Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
3
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 2023; https://doi.org/10.3390/math8112023
Received: 1 October 2020 / Revised: 10 November 2020 / Accepted: 11 November 2020 / Published: 13 November 2020
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana–Baleanu operator. Here we present solutions to simple initial value problems involving these two operators and show that, apart from some special cases, the solutions have an intrinsic discontinuity at the origin. The intrinsic nature of the discontinuity in the solution raises concerns about using such operators in modelling. Solutions to initial value problems involving the traditional Caputo operator, which has a singularity inits kernel, do not have these intrinsic discontinuities. View Full-Text
Keywords: Caputo–Fabrizio operator; Atangana–Baleanu operator; fractional falculus Caputo–Fabrizio operator; Atangana–Baleanu operator; fractional falculus
MDPI and ACS Style

Angstmann, C.N.; Jacobs, B.A.; Henry, B.I.; Xu, Z. Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators. Mathematics 2020, 8, 2023. https://doi.org/10.3390/math8112023

AMA Style

Angstmann CN, Jacobs BA, Henry BI, Xu Z. Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators. Mathematics. 2020; 8(11):2023. https://doi.org/10.3390/math8112023

Chicago/Turabian Style

Angstmann, Christopher N.; Jacobs, Byron A.; Henry, Bruce I.; Xu, Zhuang. 2020. "Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators" Mathematics 8, no. 11: 2023. https://doi.org/10.3390/math8112023

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