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Volume 7, Issue 5
Controllability of Nonlinear Fractional Systems with Multiple State and Control Delays

Mustafa Aydin

DOI: 10.12150/jnma.2025.1965

J. Nonl. Mod. Anal., 7 (2025), pp. 1965-1981.

Published online: 2025-09

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This study focuses on examining the controllability of nonlinear fractional differential systems in finite-dimensional spaces, considering multiple delays in both state and control. For linear systems, the necessary and sufficient conditions for relative controllability are established through the definition and application of the Gramian matrix. For nonlinear systems, controllability conditions are derived using Schauder’s fixed point theorem.

  • Keywords

Fractional differential system, relative controllability, multiple control delays, multiple state delays, Mittag-Leffler-type function, multivariate matrix equations.

  • AMS Subject Headings

26A33, 34A08, 93B05, 34A34

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1965, author = {Aydin , Mustafa}, title = {Controllability of Nonlinear Fractional Systems with Multiple State and Control Delays}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {5}, pages = {1965--1981}, abstract = {

This study focuses on examining the controllability of nonlinear fractional differential systems in finite-dimensional spaces, considering multiple delays in both state and control. For linear systems, the necessary and sufficient conditions for relative controllability are established through the definition and application of the Gramian matrix. For nonlinear systems, controllability conditions are derived using Schauder’s fixed point theorem.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1965}, url = {http://global-sci.org/intro/article_detail/jnma/24405.html} }
TY - JOUR T1 - Controllability of Nonlinear Fractional Systems with Multiple State and Control Delays AU - Aydin , Mustafa JO - Journal of Nonlinear Modeling and Analysis VL - 5 SP - 1965 EP - 1981 PY - 2025 DA - 2025/09 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1965 UR - https://global-sci.org/intro/article_detail/jnma/24405.html KW - Fractional differential system, relative controllability, multiple control delays, multiple state delays, Mittag-Leffler-type function, multivariate matrix equations. AB -

This study focuses on examining the controllability of nonlinear fractional differential systems in finite-dimensional spaces, considering multiple delays in both state and control. For linear systems, the necessary and sufficient conditions for relative controllability are established through the definition and application of the Gramian matrix. For nonlinear systems, controllability conditions are derived using Schauder’s fixed point theorem.

Aydin , Mustafa. (2025). Controllability of Nonlinear Fractional Systems with Multiple State and Control Delays. Journal of Nonlinear Modeling and Analysis. 7 (5). 1965-1981. doi:10.12150/jnma.2025.1965
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