Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator

Saima Rashid; Sobia Sultana; Bushra Kanwal; Fahd Jarad; Aasma Khalid; Saima Rashid; Sobia Sultana; Bushra Kanwal; Fahd Jarad; Aasma Khalid

doi:10.3934/math.2022880

AIMS Mathematics

2022, Volume 7, Issue 9: 16067-16101. doi: 10.3934/math.2022880

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Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh 12211, Saudi Arabia
3.
Department of Mathematical Sciences, Fatimah Jinnah Women's University, Rawalpindi, Pakistan
4.
Department of Mathematics, Çankaya University, Ankara, Türkiye
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
6.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
7.
Department of Mathematics, Government College Women's University, Faisalabad, Pakistan

Received: 02 April 2022 Revised: 08 June 2022 Accepted: 13 June 2022 Published: 30 June 2022
MSC : 46S40, 47H10, 54H25

Swift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming g$ {\bf H} $-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor $ \varpi\in[0, 1] $ which encompasses the varying fractional values. Finally, the EADM is predicted to be effective and precise in generating the analytical results for dynamical fuzzy fractional partial differential equations that emerge in scientific disciplines.
- Elzaki transform,
- Atangana-Baleanu fractional derivative,
- Swift-Hohenberg equation,
- statistical inference
Citation: Saima Rashid, Sobia Sultana, Bushra Kanwal, Fahd Jarad, Aasma Khalid. Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator[J]. AIMS Mathematics, 2022, 7(9): 16067-16101. doi: 10.3934/math.2022880

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Abstract

Swift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming g$ {\bf H} $-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor $ \varpi\in[0, 1] $ which encompasses the varying fractional values. Finally, the EADM is predicted to be effective and precise in generating the analytical results for dynamical fuzzy fractional partial differential equations that emerge in scientific disciplines.

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