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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2023 / Cilt: 13 - Sayı: 1

A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

Chandan Shukla
Ashwini Kumar Upadhyay
Arun Singh
Ritika Pandey
Anurag Shukla
Pages
130–138
Publication Date
2023-12-17
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, a fractional heat equation is discussed as an example.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper.
📊
Key Findings & Data:We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system.
💡
Conclusion & Impact:Finally, a fractional heat equation is discussed as an example.
🔬Design:Makale
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper. We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system. The application of well-known fixed point theorem methodologies is avoided in this paper. Finally, a fractional heat equation is discussed as an example.

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Cite This Article

Shukla, C., Upadhyay, A. K., Singh, A., Pandey, R., Shukla, A. (2023). A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 13 - Sayı: 1, 130–138. https://doi.org/10.11121/ijocta.2023.1256

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References (11)

  1. Baleanu, D., Diethelm, K., Scalas, E., & Tru- jillo, J. J. (2012). Fractional Calculus Models and Numerical Methods, Series on Complex- ity, Nonlinearity and Chaos, World Scientific Publishing, Boston, Mass, USA
  2. Lakshmikantham, V., Leela, S., & Devi, J. V. (2009). Theory of Fractional Dynamic Sys- tems, Cambridge Scientific Publishers
  3. Podlubny, I. (1999). Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to method of their solution and some of their applications, San Diego, CA: Academic Press
  4. Zhou, Y. (2015). Fractional Evolution Equa- tions and Inclusions: Analysis and Control, Elsevier, New York
  5. Mohan Raja, M., Vijayakumar, V., & Ud- hayakumar R. (2020). Results on the exis- tence and controllability of fractional integro- differential system of order 1 [6] Shukla, A., Sukavanam, N., & Pandey, D.N. (2015). Complete controllability of semi- linear stochastic system with delay. Ren- diconti del Circolo Matematico di Palermo (1952-), 64(2),209-220
  6. Shukla, A., Sukavanam, N., & Pandey, D.N. (2015). Approximate Controllability of Semi- linear Fractional Control Systems of Order α ∈ (1, 2]. In 2015 Proceedings of the Con- ference on Control and its Applications (pp. 175-180), Society for Industrial and Applied Mathematics
  7. Shukla, A., Sukavanam, N., & Pandey, D. N. (2014). Controllability of semilinear sto- chastic system with multiple delays in control. IFAC Proceedings Volumes, 47(1), 306-312
  8. Shukla, A., Sukavanam, N., & Pandey, D.N. (2018). Approximate controllability of semilinear fractional stochastic control sys- tem. Asian-European Journal of Mathemat- ics, 11(06), p.1850088
  9. Shukla, A., Vijayakumar, V., & Nisar, K.S. (2022). A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r ∈ (1, 2). Chaos, Solitons & Fractals, 154, p.111615
  10. Mohan Raja, M., Vijayakumar, V., Shukla, A., Sooppy Nisar, K., Sakthivel, N., & Kali- raj, K. (2022). Optimal control and approx- imate controllability for fractional integrod- ifferential evolution equations with infinite delay of order r ∈ (1, 2). Optimal Control Applocations and Methods, 43(4), 996-1019. DOI:
  11. Kavitha, K., Nisar, K.S., Shukla, A., Vijayakumar, V., & Rezapour S. (2021). A discussion concerning the existence re- sults for the Sobolev-type Hilfer frac- tional delay integro-differential syst