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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Vydáno v:Applied mathematics and nonlinear sciences Ročník 5; číslo 2; s. 35 - 48
Hlavní autoři: Touchent, Kamal Ait, Hammouch, Zakia, Mekkaoui, Toufik
Médium: Journal Article
Jazyk:angličtina
Vydáno: Beirut Sciendo 01.07.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Témata:
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
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Tagy: Přidat tag
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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.
AbstractList 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.
Author Mekkaoui, Toufik
Touchent, Kamal Ait
Hammouch, Zakia
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  surname: Hammouch
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  surname: Mekkaoui
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  organization: Faculty of Sciences and Techniques, Moulay Ismail University of Meknes. BP 09 Boutalamine52000Errachidia, Morocco
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Snippet In this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio...
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StartPage 35
SubjectTerms 26A33
35R11
47A15
Atangana-Baleanu fractional derivative
Caputo-Fabrizio fractional derivative
Exact solution
Modified invariant subspace method
Partial differential equations
Title A modified invariant subspace method for solving partial differential equations with non-singular kernel fractional derivatives
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