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A study on the controllability of Atangana–Baleanu Caputo fractional neutral differential equations with delay

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  • Hussain, Sadam
  • Sarwar, Muhammad
  • Shah, Syed Khayyam
  • Abodayeh, Kamaleldin
  • Ansari, Khursheed J.
  • Promsakon, Chanon
  • Sitthiwirattham, Thanin

Abstract

In this paper, we demonstrate the controllability of semilinear neutral differential equations with impulses and delays, governed by the Atangana–Baleanu (AB) Caputo fractional derivative (FD). We establish sufficient conditions for controllability by combining semigroup theory with Darbo’s fixed point theorem. The fractional-order derivative offers a more accurate representation of memory and hereditary effects, thereby enhancing the understanding of system dynamics. The challenges posed by impulsive effects and time delays are addressed using the measure of noncompactness. Two examples are presented to ensure the effectiveness and applicability of the proposed method in supporting the theoretical results. This study provides practical insights and introduces a novel analytical framework for handling complex systems described by fractional dynamics, with potential applications in engineering and physics.

Suggested Citation

  • Hussain, Sadam & Sarwar, Muhammad & Shah, Syed Khayyam & Abodayeh, Kamaleldin & Ansari, Khursheed J. & Promsakon, Chanon & Sitthiwirattham, Thanin, 2025. "A study on the controllability of Atangana–Baleanu Caputo fractional neutral differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p3:s0960077925013785
    DOI: 10.1016/j.chaos.2025.117365
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    References listed on IDEAS

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    1. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Jasmina Djordjevic & Sanja Konjik & Darko Mitrović & Andrej Novak, 2021. "Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 316-338, July.
    3. Dumitru Baleanu & Amin Jajarmi & Mojtaba Hajipour, 2017. "A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 718-737, December.
    4. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
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