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A pair of generalized \(\alpha\) -fractional variational inequality problems ( \(\alpha\) -GFVIP) and generalized \(\alpha\) -fractional dual variational inequality problems ( \(\alpha\) -GFDVIP) are presented in this study. The proven equivalence theorem applies to both the \(\alpha\) -fractional minimization problem (also known as \(\alpha\) -FMP) and the extended Caputo \(\alpha\) -fractional variational inequality problems (also known as GCFVIP). Using generalized \(\alpha\) -fractional Bregman divergence, the equivalence theorem of generalized fractional variational inequality problems (GFVIP) and generalized dual \(\alpha\) -fractional variational inequality problems ( \(\alpha\) -GDFVIP) is studied to establish Minty’s lemma in fractional calculus.

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On Existence of Generalized Fractional Variational Inequality Problems of Order \({\varvec{\alpha}}\)

  • 会议论文

  • 发表日期：

    2026年

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  • Sagarika Dash,
  • Prasanta Kumar Das,
  • Subhadarshan Sahoo

摘要

A pair of generalized \(\alpha\) -fractional variational inequality problems ( \(\alpha\) -GFVIP) and generalized \(\alpha\) -fractional dual variational inequality problems ( \(\alpha\) -GFDVIP) are presented in this study. The proven equivalence theorem applies to both the \(\alpha\) -fractional minimization problem (also known as \(\alpha\) -FMP) and the extended Caputo \(\alpha\) -fractional variational inequality problems (also known as GCFVIP). Using generalized \(\alpha\) -fractional Bregman divergence, the equivalence theorem of generalized fractional variational inequality problems (GFVIP) and generalized dual \(\alpha\) -fractional variational inequality problems ( \(\alpha\) -GDFVIP) is studied to establish Minty’s lemma in fractional calculus.