Work

Extended nonlinear variational like-inequalities driven by system of fractional evolutionary equations

Year: 2025

Type: article

Abstract: In this article, we consider an extended evolutionary system involving fractional differential variational-like inequalities. The system consists of a nonlinear mixed variational-like inequality and an extended fractional differential equation in a complete normed linear space. We examine the non-emptiness, closedness, boundedness and convexity of solution set for the considered nonlinear mixed variational-like inequality in this setting. Furthermore, we establish upper semicontinuity and measurability of set valued solution map of the mixed quasi-variational inequality with respect to both state variable and time variable. Additionally, the existence of mild solutions for the system is shown by means of fractional operator theory, Bohnenblust-Karlin fixed point theorem for multivalued mappings and operator semigroup theory. We conclude by a numerical example, with the response times for different values of α .

Source: Fixed Point Theory and Algorithms for Sciences and Engineering

DOI: 10.1186/s13663-025-00813-5

Authors: Imran Ali, Haider Abbas Rizvi, Mijanur Rahaman, Yuanheng Wang

Institutions: Koneru Lakshmaiah Education Foundation, Dhofar University, Syamaprasad College, Zhejiang Normal University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,790

Funder: National Natural Science Foundation of China