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Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness

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  • Kavitha, K.
  • Vijayakumar, V.
  • Udhayakumar, R.

Abstract

This manuscript highlights the controllability of Hilfer fractional neutral differential systems with infinite delay. A vivid study on the primary outcomes is carried out by applying fractional calculus, and for the main results, we use fixed point technique to the measures of noncompactness. The results, thus acquired, are extend to the concept of nonlocal conditions. Lastly, a model is presented for the illustration of theory.

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  • Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304331
    DOI: 10.1016/j.chaos.2020.110035
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    1. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    2. JinRong Wang & Zhenbin Fan & Yong Zhou, 2012. "Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 292-302, July.
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    5. N. I. Mahmudov, 2013. "Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, March.
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    2. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    3. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Velmurugan Subramanian & Ghada AlNemer & Ahmed M. Elshenhab, 2022. "Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(22), pages 1-18, November.
    4. Deep, Amar & Deepmala, & Hazarika, Bipan, 2021. "An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
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    6. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Jaradat, Imad & Alquran, Marwan & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2022. "Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Nisar, Kottakkaran Sooppy & Jothimani, K. & Kaliraj, K. & Ravichandran, C., 2021. "An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Muchenedi Hari Kishor & Sharifah E. Alhazmi & Shrideh Al-Omari, 2022. "A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    10. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Yang Wang & Yongyang Liu & Yansheng Liu, 2022. "Total Controllability of Non-Autonomous Measure Evolution Systems with Non-Instantaneous Impulses and State-Dependent Delay," Mathematics, MDPI, vol. 10(15), pages 1-15, July.
    12. Thitiporn Linitda & Kulandhaivel Karthikeyan & Palanisamy Raja Sekar & Thanin Sitthiwirattham, 2023. "Analysis on Controllability Results for Impulsive Neutral Hilfer Fractional Differential Equations with Nonlocal Conditions," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    13. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "A new approach on approximate controllability of fractional evolution inclusions of order 1 < r < 2 with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R. & Zhou, Yong, 2020. "A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    15. Asmae Tajani & Fatima-Zahrae El Alaoui, 2023. "Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 767-780, August.
    16. Daliang Zhao, 2023. "Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay," Mathematics, MDPI, vol. 11(19), pages 1-19, September.

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