TY - JOUR
T1 - Computational study on the dynamics of fractional order differential equations with applications
AU - Shah, Kamal
AU - Arfan, Muhammad
AU - Ullah, Aman
AU - Al-Mdallal, Qasem
AU - Ansari, Khursheed J.
AU - Abdeljawad, Thabet
N1 - Funding Information:
The fifth author extends his appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under Grant number R.G.P.2/172/42. The authors Kamal Shah and Thabet Abdeljawad would like to thank Prince Sultan university for the support through TAS research lab. The fourth author is thankful to Al Ain university, UAE for providing the financial support with Grant No. 31S363-UPAR (4) 2018.
Publisher Copyright:
© 2022 Elsevier Ltd
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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U2 - 10.1016/j.chaos.2022.111955
DO - 10.1016/j.chaos.2022.111955
M3 - Article
AN - SCOPUS:85126306760
SN - 0960-0779
VL - 157
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 111955
ER -