GENERALIZED HYERS-ULAM-RASSIAS STABILITY OF PERTURBED THIRD-ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
DOI:
https://doi.org/10.33003/fjs-2026-1009-5173Keywords:
Hyers-Ulam-Rassias stability, Nonlinear differential equations, Third order equation, Gronwall-Bellman-Bihari inequality.Abstract
This paper establishes generalized Hyers-Ulam-Rassias (H-U-R) stability results for a class of perturbed third-order nonlinear ordinary differential equations (ODEs). The paper considered family of third-order nonlinear differential equations. Under a set of specific criteria on the nonlinearities and using integral transform techniques, the problems are converted into equivalent integral equations. By applying appropriate nonlinear generalizations of the Gronwall-Bellman inequality (Bihari-type inequalities), we derive explicit bounds for the deviation of any approximate solution from an exact solution, thereby proving H-U-R stability. Explicit formulas for the Hyers-Ulam-Rassias constants are provided. The theoretical results are supported by a representative numerical example.
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