Solving fractional partial differential equations via a new scheme

In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative. We illustrate the method with a simple algorithm that can be used to solve different types of ti...

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Published inAIMS mathematics Vol. 8; no. 3; pp. 5318 - 5337
Main Authors Qazza, Ahmad, Saadeh, Rania, Salah, Emad
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
analytical solution
fractional differential equations
power series
time fractional partial differential equations
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ISSN2473-6988
2473-6988
DOI10.3934/math.2023267

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Abstract In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative. We illustrate the method with a simple algorithm that can be used to solve different types of time-fractional partial problems. We introduce a new theorem to explain the required substitutions of the proposed method. In addition, convergence analysis conditions of the method are given. Furthermore, some different illustrative examples of time-fractional partial differential equations and systems are discussed to show the applicability and simplicity of the new approach.
AbstractList In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative. We illustrate the method with a simple algorithm that can be used to solve different types of time-fractional partial problems. We introduce a new theorem to explain the required substitutions of the proposed method. In addition, convergence analysis conditions of the method are given. Furthermore, some different illustrative examples of time-fractional partial differential equations and systems are discussed to show the applicability and simplicity of the new approach.
Author Saadeh, Rania
Qazza, Ahmad
Salah, Emad
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Cites_doi 10.1016/j.physleta.2006.06.024
10.1016/j.chaos.2020.109619
10.1016/j.rinp.2020.103667
10.1016/j.physa.2020.125150
10.1016/j.rinp.2015.01.008
10.1142/p614
10.1109/TMTT.1970.1127270
10.5373/JARAM.1447.051912
10.3390/sym14010050
10.1016/j.apm.2015.10.021
10.1016/j.cam.2014.01.002
10.3390/sym12060925
10.1515/nleng-2021-0022
10.17512/jamcm.2020.1.05
10.1186/1687-1847-2013-18
10.3390/axioms12020111
10.3390/fractalfract6080419
10.1007/s11071-017-3820-7
10.1016/j.amc.2015.01.034
10.3390/e15125305
10.3390/axioms10040332
10.1016/j.nahs.2009.10.006
10.1007/978-981-15-8498-5_2
10.5899/2016/cna-00235
10.1016/j.cnsns.2010.07.016
10.1002/mma.5842
10.1201/9780203489659
10.3390/fractalfract6090490
10.1016/S0096-3003(01)00312-5
10.1002/num.22683
10.1016/j.aej.2020.03.044
10.22436/jnsa.009.11.10
10.1016/j.aej.2022.07.022
10.1016/j.aej.2020.03.029
10.3233/FI-2019-1795
10.1016/j.micromeso.2013.02.054
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key-10.3934/math.2023267-30
key-10.3934/math.2023267-31
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key-10.3934/math.2023267-10
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key-10.3934/math.2023267-11
key-10.3934/math.2023267-33
key-10.3934/math.2023267-12
key-10.3934/math.2023267-34
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key-10.3934/math.2023267-35
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key-10.3934/math.2023267-36
key-10.3934/math.2023267-15
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key-10.3934/math.2023267-16
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key-10.3934/math.2023267-17
key-10.3934/math.2023267-39
key-10.3934/math.2023267-18
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key-10.3934/math.2023267-26
key-10.3934/math.2023267-27
key-10.3934/math.2023267-28
key-10.3934/math.2023267-29
key-10.3934/math.2023267-19
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  doi: 10.1016/j.physleta.2006.06.024
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  doi: 10.1142/p614
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  doi: 10.1109/TMTT.1970.1127270
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  doi: 10.3390/sym12060925
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  doi: 10.1515/nleng-2021-0022
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  doi: 10.17512/jamcm.2020.1.05
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  doi: 10.1186/1687-1847-2013-18
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  doi: 10.3390/axioms12020111
– ident: key-10.3934/math.2023267-4
  doi: 10.3390/fractalfract6080419
– ident: key-10.3934/math.2023267-18
  doi: 10.1007/s11071-017-3820-7
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  doi: 10.1016/j.amc.2015.01.034
– ident: key-10.3934/math.2023267-17
  doi: 10.3390/e15125305
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  doi: 10.3390/axioms10040332
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  doi: 10.1016/j.nahs.2009.10.006
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  doi: 10.1007/978-981-15-8498-5_2
– ident: key-10.3934/math.2023267-25
  doi: 10.5899/2016/cna-00235
– ident: key-10.3934/math.2023267-14
  doi: 10.1016/j.cnsns.2010.07.016
– ident: key-10.3934/math.2023267-39
  doi: 10.1002/mma.5842
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  doi: 10.1201/9780203489659
– ident: key-10.3934/math.2023267-34
  doi: 10.3390/fractalfract6090490
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  doi: 10.1016/S0096-3003(01)00312-5
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  doi: 10.1002/num.22683
– ident: key-10.3934/math.2023267-10
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  doi: 10.1016/j.aej.2020.03.044
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  doi: 10.1016/j.aej.2022.07.022
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SubjectTerms analytical solution
fractional differential equations
power series
time fractional partial differential equations
Title Solving fractional partial differential equations via a new scheme
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