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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Published inApplied mathematics and nonlinear sciences Vol. 5; no. 2; pp. 35 - 48
Main Authors Touchent, Kamal Ait, Hammouch, Zakia, Mekkaoui, Toufik
Format Journal Article
LanguageEnglish
Published Beirut Sciendo 01.07.2020
De Gruyter Poland
Subjects
26A33
35R11
47A15
Atangana-Baleanu fractional derivative
Caputo-Fabrizio fractional derivative
Exact solution
Modified invariant subspace method
Partial differential equations
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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.
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ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.2.00012