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September 10, 2025

Discussion on the approximate controllability results for neutral fractional differential systems with state‐dependent delay

ADA. DhanushVellore Institute of Technology University VVV. VijayakumarVellore Institute of Technology University

Key Points

Approximate controllability is achievable under new conditions established for neutral fractional differential systems.
Sufficient conditions rely on semigroup theory and Schauder's fixed-point theorem for proving controllability.
The study incorporates delay effects, specifically state-dependent delays, in the fractional differential equations.
An example is provided that illustrates the practical application of the main theoretical results.

Abstract

Abstract This research explores the approximate controllability of a neutral fractional differential equations incorporating delay effects via almost sectorial operators. A set of sufficient conditions is established to achieve the desired results using semigroup theory associated with almost sectorial operators, Schauder's fixed‐point theorem, and fractional calculus. Then, we provide some novel conditions for the system and assume that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the main results.

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