Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line-Reference-Cited by-同舟云学术

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

Published:2024 Issue:2 Volume:9 Page:5071-5087
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Thabet Sabri T. M.¹,Kedim Imed²,Vivas-Cortez Miguel³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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