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August 21, 2025Open Access

Stabilities of Ulam-Hyers type for a class of nonlinear fractional differential equations with integral boundary conditions in Banach spaces

Key Points

Existence and uniqueness of continuously differentiable solutions is demonstrated for the given fractional differential equations.
New sufficient conditions provide a unified framework for understanding stability, specifically Ulam-Hyers stability.
This analysis utilizes integral boundary conditions within the context of Banach spaces, enhancing the understanding of fractional differential equations.
Two illustrative examples validate the proposed theoretical results, underscoring the practical application of the findings.

Abstract

Motivated by the knowledge of the existence of continuous solutions of a certain fractional boundary value problem with integral boundary conditions, we present in here-in a unified manner-new sufficient conditions to conclude the existence and uniqueness of continuously differentiable solutions to this fractional boundary value problem and analyse its stability in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. After presenting the main conclusions, two illustrative examples are provided to verify the effectiveness of the proposed theoretical results.

Stabilities of Ulam-Hyers type for a class of nonlinear fractional differential equations with integral boundary conditions in Banach spaces

Key Points

Abstract

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