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Dergiler / 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
Sayfa
130–138
Yayın Tarihi
2023-12-17
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Finally, a fractional heat equation is discussed as an example.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper.
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Temel Bulgular & Veri:We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system.
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Sonuç & Katkı:Finally, a fractional heat equation is discussed as an example.
🔬Tür:Makale
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

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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Bu Makaleye Atıf Yap

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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Kaynakça (11)

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  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
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  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