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Review

Regional Boundary Observability for Semilinear Fractional Systems with Riemann-Liouville Derivative

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Pages 420-437 | Received 09 Aug 2022, Accepted 11 Jan 2023, Published online: 15 Feb 2023

References

  • Amouroux, M., El Jai, A., Zerrik, E. H. (1994). Regional observability of distributed systems. Int. J. Syst. Sci. 25(2):301–313. DOI: 10.1080/00207729408928961.
  • Arshad, S., Baleanu, D., Tang, Y. (2019). Fractional differential equations with bio-medical applications. In Handbook of Fractional Calculus with Applications: Applications in Engineering, Life and Social Sciences, Part A. Berlin, Boston: De Gruyter, p. 1–20. DOI: 10.1515/9783110571905-001.
  • Baleanu, D., Lopes, A. M. (2019). Handbook of Fractional Calculus with Applications: Applications in Engineering, Life and Social Sciences, Part A. Berlin, Boston: De Gruyter, DOI: 10.1515/9783110571905.
  • Baleanu, D., Lopes, A. M. (2019). Handbook of Fractional Calculus with Applications: Applications in Engineering, Life and Social Sciences, Part B. Berlin, Boston: De Gruyter, DOI: 10.1515/9783110571929.
  • Boutoulout, A., Bourray, H., El Alaoui, F. Z. (2010). Regional boundary observability for semi-linear systems approach and simulation. Int. J. Math. Analys. 4(24):1153–1173.
  • Curtain, R. F., Zwart, H. (1995). An Introduction to Infinite-Dimensional Linear Systems Theory. New York: Springer-Verlag,
  • El Alaoui, F. Z., Boutoulout, A., Zguaid, K. (2021). Regional reconstruction of semilinear caputo type time-fractional systems using the analytical approach. Adv. Theory Nonlinear Analysis Its Appl. 5(4):580–599. DOI: 10.31197/atnaa.799236.
  • Jai, A. E. (1997). Capteurs et Actionneurs Dans L’analyse Des Systèmes Distribués. Paris u.a: Elsevier Masson.
  • Ge, F., Chen Quan, Y., Kou, C. (2018). Regional Analysis of Time-Fractional Diffusion Processes. Switzerland: Springer International Publishing, DOI: 10.1007/978-3-319-72896-4.
  • He, J. W., Zhou, Y. (2022). Hölder regularity for non-autonomous fractional evolution equations. Fract. Calc. Appl. Anal. 25(2):378–407. DOI: 10.1007/s13540-022-00019-1.
  • Hilfer, R. (2000). Applications of Fractional Calculus in Physics. Singapore; River Edge, NJ: World Scientific Publishing Company.
  • Kilbas, A. A., Srivastava, H. M., Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations. Boston: Elsevier Science Ltd,
  • Louartassi, Y., El Mazoudi, E. H., Elalami, N. (2012). A new generalization of Lemma Gronwall-Bellman. Applied Mathematical Sciences. 6(13):621–628.
  • Oldham, K. B., Spanier, J. (1974). Fractional Calculus, 1st edition. New York: Elsevier Science,
  • Petráš, I. (2019). Handbook of Fractional Calculus with Applications: Applications in Control. Berlin, Boston: De Gruyter, DOI: 10.1515/9783110571745.
  • Samko, S. G., Kilbas, A. A., Marichev, O. I. (1993). Fractional Integrals and Derivatives: Theory and Applications, 1 edition. Philadelphia, USA: CRC Press,
  • Tarasov, V. E. (2019). Handbook of Fractional Calculus with Applications: Applications in Physics, Part A. Berlin, Boston: De Gruyter, DOI: 10.1515/9783110571707.
  • Tarasov, V. E. (2019). Handbook of Fractional Calculus with Applications: Applications in Physics, Part B. Berlin, Boston: De Gruyter, DOI: 10.1515/9783110571721.
  • Tucsnak, M., Weiss, G. (2009). Observation and control for operator semigroups. Basel: Birkhäuser. doi; DOI: 10.1007/978-3-7643-8994-9.
  • Zerrik, E., Badraoui, L. (2000). Sensor characterization for regional boundary observability. Int. J. Appl. Math. Comput. Sci. 10(2):345–356.
  • Zerrik, E., Badraoui, L., El Jai, A. (1999). Sensors and regional boundary state reconstruction of parabolic systems. Sens. Actuators A. 75(2):102–117. DOI: 10.1016/S0924-4247(98)00293-3.
  • Zerrik, E., Bourray, H., Boutoulout, A. (2002). Regional boundary observability: a numerical approach. Int. J. Appl. Math. Comput. Sci. 12(2):143–151.
  • Zerrik, E., Bourray, H., El Jai, A. (2004). Regional observability for semilinear distributed parabolic systems. J. Dyn. Control Syst. 10(3):413–430. DOI: 10.1023/B:JODS.0000034438.72863.ca.
  • Zguaid, K., El Alaoui, F. Z., Boutoulout, A. (2021). Regional observability of linear fractional systems involving riemann-liouville fractional derivative. In: eds., Z. Hammouch, H. Dutta, S. Melliani, and M. Ruzhansky, Nonlinear analysis: Problems, applications and computational methods. Switzerland: Springer International Publishing, p. 164–178.
  • Zguaid, K., El Alaoui, F. Z., Boutoulout, A. (2021). Regional observability for linear time fractional systems. Math. Comput. Simul. 185:77–87. DOI: 10.1016/j.matcom.2020.12.013.
  • Zguaid, K., El Alaoui, F. Z. (2022). Regional boundary observability for Riemann–Liouville linear fractional evolution systems. Math. Comput. Simul. 199:272–286. DOI: 10.1016/j.matcom.2022.03.023.
  • Zguaid, K., El Alaoui, F. Z. (2022). Regional boundary observability for linear time-fractional systems. Part. Different. Equat. Appl. Math. 6:100432. DOI: 10.1016/j.padiff.2022.100432.
  • Zhou, Y. (2022). Infinite interval problems for fractional evolution equations. Mathematics. 10(6):900. DOI: 10.3390/math10060900.
  • Zhou, Y., He, J. W. (2022). A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. Fract. Calc. Appl. Anal. 25(3):924–961. DOI: 10.1007/s13540-022-00057-9.
  • Zhou, Y., Zhang, L., Shen, X. H. (2013). Existence of mild solutions for fractional evolution equations. J. Integral Equat. Appl. 25(4):557–586. DOI: 10.1216/JIE-2013-25-4-557.

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