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Bingzhi Sun, Shuqin Zhang, Tianhu Yu, Shanshan Li. SOLVABILITY OF SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTIONAL BOUNDARY VALUE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1882-1902. doi: 10.11948/20240268
Citation: Bingzhi Sun, Shuqin Zhang, Tianhu Yu, Shanshan Li. SOLVABILITY OF SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTIONAL BOUNDARY VALUE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1882-1902. doi: 10.11948/20240268
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SOLVABILITY OF SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTIONAL BOUNDARY VALUE CONDITIONS

  • 1.

    School of Mathematical Sciences, Luoyang Normal University, 471934 Luoyang, China

  • 2.

    Department of Mathematics, China University of Mining and Technology, Beijing, China

  • 3.

    School of Mathematics and Information Sciences, Yantai University, 264005 Yantai, China

  • Author Bio: Email: 108842@cumtb.edu.cn(S. Zhang); Email: yuthjianyang@yeah.net(T. Yu); Email: shanhuyuli@163.com(S. Li)
  • Corresponding author: Email: bingzhi93@qq.com(Bingzhi Sun) 
  • Fund Project: This work was supported by the Natural Science Foundation of China (12071302), National Natural Science Foundation of China (Grant No. 12372013), Natural Science Foundation of Henan (Grant No. 242300421166), Program for Science and Technology Innovation Talents in Universities of Henan Province, China (Grant No. 24HASTIT034), Key Scientific Research Projects of Universities in Henan Province (Grant No. 25B110004), Natural Science Foundation of Henan (Grant No. 232300420122)
    Abstract

  • The purpose of this paper is to develop the existence theory for a functional boundary problem of sequential fractional differential equations involving Caputo fractional derivatives of order $ \alpha+1 $ with $ n-1<\alpha\leq n $. The main goal of the current contribution is to use Mawhin's coincidence degree theory and a few novel operators to derive sufficient criteria for the existence of solutions to the resonance problems at hand. An example that is relevant is given to support the findings.

    MSC: 34A08, 34B15
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