TY - JOUR
T1 - Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line
AU - Thabet, Sabri T.M.
AU - Kedim, Imed
AU - Vivas-Cortez, Miguel
N1 - Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
PY - 2024/1/24
Y1 - 2024/1/24
N2 - 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.
AB - 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.
KW - Bagley-Torvik equation
KW - fixed point theorems
KW - fractional derivatives
KW - unbounded solutions
UR - http://www.scopus.com/inward/record.url?scp=85186553688&partnerID=8YFLogxK
U2 - 10.3934/math.2024246
DO - 10.3934/math.2024246
M3 - Article
SN - 2473-6988
VL - 9
SP - 5071
EP - 5087
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 2
ER -