Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line

Sabri T. M. Thabet; Imed Kedim; Miguel Vivas-Cortez; Sabri T. M. Thabet; Imed Kedim; Miguel Vivas-Cortez

doi:10.3934/math.2024246

AIMS Mathematics

2024, Volume 9, Issue 2: 5071-5087. doi: 10.3934/math.2024246

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Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line

1.
Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen
2.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
3.
Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador

Received: 03 December 2023 Revised: 22 December 2023 Accepted: 02 January 2024 Published: 24 January 2024
MSC : 34A08, 34B15

The fractional Bagley-Torvik system (FBTS) is initially created by utilizing fractional calculus to study the demeanor of real materials. It can be described as the dynamics of an inflexible plate dipped in a Newtonian fluid. In the present article, we aim for the first time to discuss the existence and uniqueness (E&U) theories of an unbounded solution for the proposed generalized FBTS involving Riemann-Liouville fractional derivatives in the half-line $ (0, \infty) $, by using fixed point theorems (FPTs). Moreover, the Hyers-Ulam stability (HUS), Hyers-Ulam-Rassias stability (HURS), and semi-Hyers-Ulam-Rassias stability (sHURS) are proved. Finally, two numerical examples are given for checking the validity of major findings. By investigating unbounded solutions for the FBTS, engineers gain a deeper understanding of the underlying physics, optimize performance, improve system design, and ensure the stability of the motion of real materials in a Newtonian fluid.
- fractional derivatives,
- Bagley-Torvik equation,
- fixed point theorems,
- unbounded solutions
Citation: Sabri T. M. Thabet, Imed Kedim, Miguel Vivas-Cortez. Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line[J]. AIMS Mathematics, 2024, 9(2): 5071-5087. doi: 10.3934/math.2024246

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Abstract

The fractional Bagley-Torvik system (FBTS) is initially created by utilizing fractional calculus to study the demeanor of real materials. It can be described as the dynamics of an inflexible plate dipped in a Newtonian fluid. In the present article, we aim for the first time to discuss the existence and uniqueness (E&U) theories of an unbounded solution for the proposed generalized FBTS involving Riemann-Liouville fractional derivatives in the half-line $ (0, \infty) $, by using fixed point theorems (FPTs). Moreover, the Hyers-Ulam stability (HUS), Hyers-Ulam-Rassias stability (HURS), and semi-Hyers-Ulam-Rassias stability (sHURS) are proved. Finally, two numerical examples are given for checking the validity of major findings. By investigating unbounded solutions for the FBTS, engineers gain a deeper understanding of the underlying physics, optimize performance, improve system design, and ensure the stability of the motion of real materials in a Newtonian fluid.

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