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A generalized Z-number approach to solvability, best approximation, and Ulam–Hyers–Rassias stability of Ψ-Hilfer fractional differential equations

Year: 2026

Type: article

Abstract: This paper investigates the solvability, best approximation, and Ulam–Hyers–Rassias stability of a class of Ψ-Hilfer fractional Hammerstein integro-differential equations in a generalized Z-number setting. The generalized Z-number framework is used to describe uncertainty together with the reliability of the available information. By applying a fixed-point approach in a generalized metric space, sufficient conditions for the existence and uniqueness of solutions are established, together with best-approximation estimates and Ulam–Hyers–Rassias stability results. An illustrative example is provided to verify the main assumptions and the corresponding contraction condition, demonstrating the applicability of the theoretical results.

Source: Boundary Value Problems

DOI: 10.1186/s13661-026-02373-y

Authors: Alireza Hatami, Reza Saadati, H. M. Srivastava, Donal O’Regan

Institutions: Iran University of Science and Technology, Ollscoil na Gaillimhe – University of Galway

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,890

OpenAlex ID: W7215705107

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