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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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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  givenname: Zakia
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  givenname: Toufik
  surname: Mekkaoui
  fullname: Mekkaoui, Toufik
  organization: Faculty of Sciences and Techniques, Moulay Ismail University of Meknes. BP 09 Boutalamine52000Errachidia, Morocco
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Cites_doi 10.1016/j.amc.2017.08.048
10.1201/9781420011623
10.1016/j.chaos.2018.01.002
10.1016/j.amc.2018.04.025
10.1016/j.camwa.2013.05.006
10.1515/fca-2017-0024
10.1186/s13662-018-1680-1
10.14419/ijpr.v1i2.849
10.3390/fractalfract2030022
10.1515/fca-2015-0010
10.1142/9789814355216
10.1016/j.camwa.2009.06.020
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2024050212243046936_j_amns.2020.2.00012_ref_001_w2aab3b7d190b1b6b1ab2ab1Aa
2024050212243046936_j_amns.2020.2.00012_ref_003_w2aab3b7d190b1b6b1ab2ab3Aa
2024050212243046936_j_amns.2020.2.00012_ref_017_w2aab3b7d190b1b6b1ab2ac17Aa
2024050212243046936_j_amns.2020.2.00012_ref_005_w2aab3b7d190b1b6b1ab2ab5Aa
2024050212243046936_j_amns.2020.2.00012_ref_010_w2aab3b7d190b1b6b1ab2ac10Aa
2024050212243046936_j_amns.2020.2.00012_ref_007_w2aab3b7d190b1b6b1ab2ab7Aa
2024050212243046936_j_amns.2020.2.00012_ref_022_w2aab3b7d190b1b6b1ab2ac22Aa
2024050212243046936_j_amns.2020.2.00012_ref_011_w2aab3b7d190b1b6b1ab2ac11Aa
2024050212243046936_j_amns.2020.2.00012_ref_009_w2aab3b7d190b1b6b1ab2ab9Aa
2024050212243046936_j_amns.2020.2.00012_ref_021_w2aab3b7d190b1b6b1ab2ac21Aa
2024050212243046936_j_amns.2020.2.00012_ref_013_w2aab3b7d190b1b6b1ab2ac13Aa
2024050212243046936_j_amns.2020.2.00012_ref_002_w2aab3b7d190b1b6b1ab2ab2Aa
2024050212243046936_j_amns.2020.2.00012_ref_016_w2aab3b7d190b1b6b1ab2ac16Aa
2024050212243046936_j_amns.2020.2.00012_ref_004_w2aab3b7d190b1b6b1ab2ab4Aa
2024050212243046936_j_amns.2020.2.00012_ref_006_w2aab3b7d190b1b6b1ab2ab6Aa
2024050212243046936_j_amns.2020.2.00012_ref_018_w2aab3b7d190b1b6b1ab2ac18Aa
2024050212243046936_j_amns.2020.2.00012_ref_008_w2aab3b7d190b1b6b1ab2ab8Aa
2024050212243046936_j_amns.2020.2.00012_ref_019_w2aab3b7d190b1b6b1ab2ac19Aa
2024050212243046936_j_amns.2020.2.00012_ref_012_w2aab3b7d190b1b6b1ab2ac12Aa
2024050212243046936_j_amns.2020.2.00012_ref_020_w2aab3b7d190b1b6b1ab2ac20Aa
2024050212243046936_j_amns.2020.2.00012_ref_014_w2aab3b7d190b1b6b1ab2ac14Aa
References_xml – ident: 2024050212243046936_j_amns.2020.2.00012_ref_001_w2aab3b7d190b1b6b1ab2ab1Aa
  doi: 10.1016/j.amc.2017.08.048
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_017_w2aab3b7d190b1b6b1ab2ac17Aa
  doi: 10.1201/9781420011623
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_019_w2aab3b7d190b1b6b1ab2ac19Aa
  doi: 10.1016/j.chaos.2018.01.002
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_002_w2aab3b7d190b1b6b1ab2ab2Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_016_w2aab3b7d190b1b6b1ab2ac16Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_003_w2aab3b7d190b1b6b1ab2ab3Aa
  doi: 10.1016/j.amc.2018.04.025
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_022_w2aab3b7d190b1b6b1ab2ac22Aa
  doi: 10.1016/j.camwa.2013.05.006
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_005_w2aab3b7d190b1b6b1ab2ab5Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_020_w2aab3b7d190b1b6b1ab2ac20Aa
  doi: 10.1515/fca-2017-0024
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_011_w2aab3b7d190b1b6b1ab2ac11Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_021_w2aab3b7d190b1b6b1ab2ac21Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_010_w2aab3b7d190b1b6b1ab2ac10Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_007_w2aab3b7d190b1b6b1ab2ab7Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_004_w2aab3b7d190b1b6b1ab2ab4Aa
  doi: 10.1186/s13662-018-1680-1
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_014_w2aab3b7d190b1b6b1ab2ac14Aa
  doi: 10.14419/ijpr.v1i2.849
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_006_w2aab3b7d190b1b6b1ab2ab6Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_015_w2aab3b7d190b1b6b1ab2ac15Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_013_w2aab3b7d190b1b6b1ab2ac13Aa
  doi: 10.3390/fractalfract2030022
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_018_w2aab3b7d190b1b6b1ab2ac18Aa
  doi: 10.1515/fca-2015-0010
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_008_w2aab3b7d190b1b6b1ab2ab8Aa
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_009_w2aab3b7d190b1b6b1ab2ab9Aa
  doi: 10.1142/9789814355216
– ident: 2024050212243046936_j_amns.2020.2.00012_ref_012_w2aab3b7d190b1b6b1ab2ac12Aa
  doi: 10.1016/j.camwa.2009.06.020
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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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