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<p>In this paper, we apply Babenko’s method to some new integral equations involving a class of fractional integral operators introduced and studied in [J. Appl. Anal. Comput. 6 (4) (2016), 981–999]. We establish the existence and uniqueness theorem as well as the Hyers-Ulam stability for certain forms of fractional integral equations. In addition, we further develop the theory for this class of fractional integral operators and show precisely that such considerations provide a class of integral operators which are related to the integral operators involving certain new forms of Sonine kernels. Several consequences of the results presented in this paper are also mentioned.</p>

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Applications of Babenko’s method to a class of integral equations

  • 期刊论文

  • 发表日期：

    2025年10月7日

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  • Min-Jie Luo,
  • Ravinder Krishna Raina,
  • Xue-Lin Zhou

摘要

In this paper, we apply Babenko’s method to some new integral equations involving a class of fractional integral operators introduced and studied in [J. Appl. Anal. Comput. 6 (4) (2016), 981–999]. We establish the existence and uniqueness theorem as well as the Hyers-Ulam stability for certain forms of fractional integral equations. In addition, we further develop the theory for this class of fractional integral operators and show precisely that such considerations provide a class of integral operators which are related to the integral operators involving certain new forms of Sonine kernels. Several consequences of the results presented in this paper are also mentioned.