Computational study on the dynamics of fractional order differential equations with applications

Kamal Shah; Muhammad Arfan; Aman Ullah; Qasem Al-Mdallal; Khursheed J. Ansari; Thabet Abdeljawad

doi:10.1016/j.chaos.2022.111955

Computational study on the dynamics of fractional order differential equations with applications

Kamal Shah, Muhammad Arfan, Aman Ullah, Qasem Al-Mdallal, Khursheed J. Ansari, Thabet Abdeljawad

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

79 Citations (Scopus)

Abstract

In this research work, the analysis of general fractional order system is investigated under Atangana, Baleanu and Caputo (ABC) fractional order derivative. Our study is related to three aspects including existence theory, stability and numerical analysis. For existence theory, we use Krasnoselskii and Banach contraction theorems. Further using nonlinear analysis, we develop some necessary results for Ulam Hyer's (UH) stability. The approximate solution is computed by using Adam's-Bashforth numerical technique. For justification, we provide three concert examples along with necessary numerical and graphical interpretations.

Original language	English
Article number	111955
Journal	Chaos, Solitons and Fractals
Volume	157
DOIs	https://doi.org/10.1016/j.chaos.2022.111955
Publication status	Published - Apr 2022

Keywords

Adam's-Bashforth method
Existence and uniqueness
Fractional general problems
Ulam Hyer's stability

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1016/j.chaos.2022.111955

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abstract = "In this research work, the analysis of general fractional order system is investigated under Atangana, Baleanu and Caputo (ABC) fractional order derivative. Our study is related to three aspects including existence theory, stability and numerical analysis. For existence theory, we use Krasnoselskii and Banach contraction theorems. Further using nonlinear analysis, we develop some necessary results for Ulam Hyer's (UH) stability. The approximate solution is computed by using Adam's-Bashforth numerical technique. For justification, we provide three concert examples along with necessary numerical and graphical interpretations.",

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AU - Shah, Kamal

AU - Arfan, Muhammad

AU - Ullah, Aman

AU - Al-Mdallal, Qasem

AU - Ansari, Khursheed J.

AU - Abdeljawad, Thabet

PY - 2022/4

Y1 - 2022/4

N2 - In this research work, the analysis of general fractional order system is investigated under Atangana, Baleanu and Caputo (ABC) fractional order derivative. Our study is related to three aspects including existence theory, stability and numerical analysis. For existence theory, we use Krasnoselskii and Banach contraction theorems. Further using nonlinear analysis, we develop some necessary results for Ulam Hyer's (UH) stability. The approximate solution is computed by using Adam's-Bashforth numerical technique. For justification, we provide three concert examples along with necessary numerical and graphical interpretations.

AB - In this research work, the analysis of general fractional order system is investigated under Atangana, Baleanu and Caputo (ABC) fractional order derivative. Our study is related to three aspects including existence theory, stability and numerical analysis. For existence theory, we use Krasnoselskii and Banach contraction theorems. Further using nonlinear analysis, we develop some necessary results for Ulam Hyer's (UH) stability. The approximate solution is computed by using Adam's-Bashforth numerical technique. For justification, we provide three concert examples along with necessary numerical and graphical interpretations.

KW - Adam's-Bashforth method

KW - Existence and uniqueness

KW - Fractional general problems

KW - Ulam Hyer's stability

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Computational study on the dynamics of fractional order differential equations with applications

Abstract

Keywords

ASJC Scopus subject areas

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