TY - JOUR
T1 - Efficient results on fractional Langevin-Sturm-Liouville problem via generalized Caputo-Atangana-Baleanu derivatives
AU - Thabet, Sabri T.M.
AU - Boutiara, Abdelatif
AU - Samei, Mohammad Esmael
AU - Kedim, Imed
AU - Vivas-Cortez, Miguel
N1 - Publisher Copyright:
© 2024 Thabet et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2024/10
Y1 - 2024/10
N2 - In this paper, we investigate the generalized Langevin-Sturm-Liouville differential problems involving Caputo-Atangana-Baleanu fractional derivatives of higher orders with respect to another positive, increasing function denoted by ρ. The fixed point theorems in the framework of Kransnoselskii and Banach are utilized to discuss the existence and uniqueness of the results. In addition, the stability criteria of Ulam-Hyers, generalize Ulam-Hyers, Ulam-Hyers-Rassias, and generalize Ulam-Hyers-Rassias are investigated by non-linear analysis besides fractional calculus. Finally, illustrative examples are reinforced by tables and graphics to describe the main achievements.
AB - In this paper, we investigate the generalized Langevin-Sturm-Liouville differential problems involving Caputo-Atangana-Baleanu fractional derivatives of higher orders with respect to another positive, increasing function denoted by ρ. The fixed point theorems in the framework of Kransnoselskii and Banach are utilized to discuss the existence and uniqueness of the results. In addition, the stability criteria of Ulam-Hyers, generalize Ulam-Hyers, Ulam-Hyers-Rassias, and generalize Ulam-Hyers-Rassias are investigated by non-linear analysis besides fractional calculus. Finally, illustrative examples are reinforced by tables and graphics to describe the main achievements.
UR - http://www.scopus.com/inward/record.url?scp=85205528392&partnerID=8YFLogxK
U2 - 10.1371/journal.pone.0311141
DO - 10.1371/journal.pone.0311141
M3 - Article
C2 - 39356680
AN - SCOPUS:85205528392
SN - 1932-6203
VL - 19
JO - PLoS ONE
JF - PLoS ONE
IS - 10
M1 - e0311141
ER -