Work

Existence, Uniqueness, and Hyers–Ulam’s Stability of the Nonlinear Bagley–Torvik Equation with Functional Initial Conditions

Year: 2026

Type: article

Abstract: The nonlinear Bagley–Torvik equation is of fundamental importance, as it captures a realistic and intricate interplay among memory effects, nonlinearity, and functional dependence—making it a powerful model for a wide range of natural and engineered systems. Its analysis contributes significantly to both the theoretical development of fractional differential equations and their practical applications across science and technology. In this paper, we employ the inverse operator method, the multivariate Mittag-Leffler function, and several classical fixed-point theorems to establish sufficient conditions for the existence, uniqueness, and Hyers–Ulam stability of solutions to the nonlinear Bagley–Torvik equation with functional initial conditions. Finally, we present several examples by explicitly computing values of the multivariate Mittag-Leffler functions to illustrate the main results.

Source: Mathematics

DOI: 10.3390/math14020286

Authors: Chenkuan Li, Wenyuan Liao, Ying-Ying Ou

Institutions: Brandon University, University of Calgary

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Natural Sciences and Engineering Research Council of Canada