Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application

Hasib Khan; Jehad Alzabut; Dumitru Baleanu; Ghada Alobaidi; Mutti-Ur Rehman; Hasib Khan; Jehad Alzabut; Dumitru Baleanu; Ghada Alobaidi; Mutti-Ur Rehman

doi:10.3934/math.2023334

AIMS Mathematics

2023, Volume 8, Issue 3: 6609-6625. doi: 10.3934/math.2023334

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Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application

1.
Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
2.
Department of Mathematics, Shaheed Benazir Bhutto Uniersity, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan
3.
Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Turkey
4.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
5.
Institute of Space Science, Magurele-Bucharest, Romania
6.
Lebanese American University, Beirut, Lebanon
7.
Department of Mathematics and Statistics, American University of Sharjah, PO Box 26666, Sharjah, United Arab Emirates
8.
Department of Mathematics, Akfa University, Tashkent, Uzbekistan
9.
Department of Mathematics, Sukkur IBA University, Sukkur, Pakistan

Received: 19 October 2022 Revised: 28 November 2022 Accepted: 12 December 2022 Published: 05 January 2023
MSC : 34A08, 49J15, 65P99

In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange's interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.
- modified ABC-operator,
- hybrid fractional differential equations,
- existence of solutions, unique solution,
- Hyers-Ulam-stability,
- numerical simulations
Citation: Hasib Khan, Jehad Alzabut, Dumitru Baleanu, Ghada Alobaidi, Mutti-Ur Rehman. Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application[J]. AIMS Mathematics, 2023, 8(3): 6609-6625. doi: 10.3934/math.2023334

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Abstract

In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange's interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.

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