@article{Thabet2024, 
author = {Sabri T. M. Thabet and Imed Kedim and Miguel Vivas-Cortez},
title = {Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {5071-5087},
keywords = {fractional derivatives, Bagley-Torvik equation, fixed point theorems, unbounded solutions},
url = {https://www.sciopen.com/article/10.3934/math.2024246},
doi = {10.3934/math.2024246},
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  ,  ∞  ), 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.}
}