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A new fuzzy fractional differential variational inequality with integral boundary conditions

Zengbao Wu, Quanguo Zhang, Tao Chen, Yibin Xiao, Tianyin Wang, Chunyan Yang

Abstract

This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in Euclidean spaces. Such a model captures the desired features of both fuzzy fractional differential inclusions with integral boundary conditions and fractional differential variational inequalities within the same framework. The existence of solutions for such a novel system is obtained under different conditions. Moreover, a numerical example is provided to illustrate our abstract results.

A new fuzzy fractional differential variational inequality with integral boundary conditions

Abstract

This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in Euclidean spaces. Such a model captures the desired features of both fuzzy fractional differential inclusions with integral boundary conditions and fractional differential variational inequalities within the same framework. The existence of solutions for such a novel system is obtained under different conditions. Moreover, a numerical example is provided to illustrate our abstract results.

Paper Structure

This paper contains 5 sections, 10 theorems, 88 equations.

Key Result

Lemma 2.1

Consider two measurable set-valued mappings $F_{1}, F_{2}:[0,T]\rightarrow 2^{R^n}$ with compact values. Suppose $f_1:[0,T]\rightarrow R^n$ is a measurable selection of $F_1$. Then there exists another measurable selection $f_2:[0,T]\rightarrow R^n$ of $F_2$ satisfying for all $s\in [0,T]$, where $H$ denotes the Hausdorff distance.

Theorems & Definitions (18)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.1
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Remark 3.1
  • Lemma 3.1
  • Remark 3.2
  • ...and 8 more