Weak noncompactness in fractional differential boundary problems: existence results

Document Type : Research Paper

Authors

Department of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran

Abstract

This paper addresses the existence of solutions for a class of fractional differential boundary value problems. The main novelty of this paper lies in providing a new analytical framework to prove solution existence for this class of equations. Our approach is grounded in a combination of a Krasnoselskii-type fixed point theorem with the concept of the measure of weak noncompactness (MWNC) in the Banach space $L^{1}(I)$. This technique allows us to prove existence under more general growth conditions than in previous works that relied  on complete continuity. By establishing a set of sufficient conditions, we demonstrate that the boundary value problem under consideration admits at least one solution. Several illustrative examples are presented to highlight the applicability and effectiveness of the obtained results.

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References

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History

  • Receive Date: 18 August 2025
  • Revise Date: 18 November 2025
  • Accept Date: 27 December 2025

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