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A coupled system of nonlinear Caputo–Hadamard Langevin equations associated with nonperiodic boundary conditions
Author(s) -
Matar Mohammed M.,
Alzabut Jehad,
Jonnalagadda Jagan Mohan
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6711
Subject(s) - hadamard transform , mathematics , uniqueness , nonlinear system , stability (learning theory) , boundary value problem , fractional calculus , mathematical analysis , fixed point theorem , langevin equation , derivative (finance) , boundary (topology) , statistical physics , physics , computer science , quantum mechanics , machine learning , financial economics , economics
In this paper, we study the coupled system of nonlinear Langevin equations involving Caputo–Hadamard fractional derivative and subject to nonperiodic boundary conditions. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the features of the Hadamard fractional derivative, the implementation of fixed point theorems, and the employment of Urs's stability approach. An example is introduced to facilitate the understanding of the theoretical findings.