Fractional partial differential variational inequality

TL;DR

This paper introduces a new class of fractional partial differential variational inequalities (FPDVI), develops a theoretical framework for their analysis, and proves the existence of smooth solutions using advanced mathematical tools.

Contribution

It is the first to study FPDVI involving fractional derivatives and nonlocal conditions, providing a comprehensive existence theory for solutions.

Findings

Established existence of smooth solutions for FPDVI

Developed a framework using Mittag-Leffler functions and fixed-point theory

Extended the analysis to nonlocal and fractional derivative contexts

Abstract

In this present paper, we introduce and study a dynamical systems involving fractional derivative operator and nonlocal condition, which is constituted of a fractional evolution equation and a time-dependent variational inequality, and is named as fractional partial differential variational inequality (FPDVI, for short). By employing the estimates involving the one-and two-parameter Mittag-Leffler functions, fixed-point theory for set-value mappings, and non-compactness measure theory, we develop a general framework to establish the existence of smooth solutions to (FPDVI).