<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives. The exact solutions are obtained by solving the reduced systems of constructed fractional differential equations. The results show that this method is very simple and effective for constructing explicit exact solutions for partial differential equations involving new fractional derivatives with nonlocal and non-singular kernels, such solutions are very useful to validate new numerical methods constructed for solving partial differential equations with CF and AB fractional derivatives.</p></abstract>

In this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives. The exact solutions are obtained by solving the reduced systems of constructed fractional differential equations. The results show that this method is very simple and effective for constructing explicit exact solutions for partial differential equations involving new fractional derivatives with nonlocal and non-singular kernels, such solutions are very useful to validate new numerical methods constructed for solving partial differential equations with CF and AB fractional derivatives.

A modified invariant subspace method for solving partial differential equations with non-singular kernel fractional derivatives

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio...

A modified invariant subspace method for solving partial differential equations with non-singular kernel fractional derivatives

Published Online: Jul 01, 2020

Page range: 35 - 48

Received: Feb 16, 2019

Accepted: Aug 28, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00012

Keywords
Modified invariant subspace method, Caputo-Fabrizio fractional derivative, Atangana-Baleanu fractional derivative, Exact solution, Partial differential equations

© 2020 Kamal Ait Touchent et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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A modified invariant subspace method for solving partial differential equations with non-singular kernel fractional derivatives

Published Online: Jul 01, 2020

Page range: 35 - 48

Received: Feb 16, 2019

Accepted: Aug 28, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00012

KeywordsModified invariant subspace method, Caputo-Fabrizio fractional derivative, Atangana-Baleanu fractional derivative, Exact solution, Partial differential equations

© 2020 Kamal Ait Touchent et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Keywords
Modified invariant subspace method, Caputo-Fabrizio fractional derivative, Atangana-Baleanu fractional derivative, Exact solution, Partial differential equations