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

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...

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Bibliographic Details
Published in:	Applied mathematics and nonlinear sciences Vol. 5; no. 2; pp. 35 - 48
Main Authors:	Touchent, Kamal Ait, Hammouch, Zakia, Mekkaoui, Toufik
Format:	Journal Article
Language:	English
Published:	Beirut Sciendo 01.07.2020 De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:	26A33 35R11 47A15 Atangana-Baleanu fractional derivative Caputo-Fabrizio fractional derivative Exact solution Modified invariant subspace method Partial differential equations
ISSN:	2444-8656, 2444-8656
Online Access:	Get full text
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Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	2444-8656 2444-8656
DOI:	10.2478/amns.2020.2.00012