Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph

• Lihong Zhang ^[1] ; Xuehui Liu ^[2]
  1. [1] Shanxi Normal University & Western Caspian University
  2. [2] Shanxi Normal University
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
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• Resumen

  • Circular network structure is widely used in neural network, image processing, computer vision and bioinformatics. For example, recurrent neural network is a kind of neural network with a circular structure that can be used to process temporal data. It has a wide range of applications in natural language processing, speech recognition, music generation, etc. In this paper, in order to reduce the complexity of the presentation, we study a class of Hilfer-type fractional differential system and differential inclusion with coupled integral boundary value conditions on the simplest circular graph. First, two existence results of Hilfer-type fractional differential system are proved by some known fixed point theorems. Further, the existence results of convex and non-convex multivalued mappings are obtained by using Leray–Schauder nonlinear alternative and Covitz–Nadler fixed point theorem, respectively. At last, two examples are given to verify our theoretical results.