Title: Existence and trajectory controllability of fractional order evolution systems driven by almost sectorial operators

Authors: Dibyajyoti Hazarika; Jayanta Borah

Addresses: Department of Mathematics, North Lakhimpur University, Assam, 787001, India ' Department of Mathematical Sciences, Tezpur University, Assam, 78028, India

Abstract: Trajectory controllability represents the strongest form of controllability and has a wide range of applications. This notion has been extensively studied by many researchers for various types of evolution systems. However, to the best of our knowledge, no work in the existing literature has addressed trajectory controllability for evolution systems governed by almost sectorial operators. Motivated by this gap, the present article establishes sufficient conditions for the trajectory controllability of a class of fractional integro-differential evolution systems driven by almost sectorial operators. In our study, both systems with and without state delays are considered. The fractional derivatives involved are of order r ∈ (0, 1) in the Caputo sense. Existence results are obtained using the Banach fixed point theorem, while the controllability results rely on tools such as properties of Mittag-Leffler functions, Gronwall's inequality, functions of type (M), and other key results from fractional calculus and functional analysis. To further support the theoretical findings, illustrative examples are provided.

Keywords: trajectory controllability; fractional differential equation; FDE; integro-differential system; almost sectorial operator; state delay.

DOI: 10.1504/IJDSDE.2026.154406

International Journal of Dynamical Systems and Differential Equations, 2026 Vol.15 No.1, pp.19 - 36

Received: 19 Oct 2024
Accepted: 06 Jan 2026
Published online: 26 Jun 2026 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article