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

Christopher Nicholas Angstmann, Byron Alexander Jacobs, Bruce Ian Henry and Zhuang Xu
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Christopher Nicholas Angstmann: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Byron Alexander Jacobs: Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
Bruce Ian Henry: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Zhuang Xu: School of Physics, University of New South Wales, Sydney, NSW 2052, Australia

Mathematics, 2020, vol. 8, issue 11, 1-16

Abstract: 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.

Keywords: Caputo–Fabrizio operator; Atangana–Baleanu operator; fractional falculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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