Exact Controllability of Hilfer Fractional Differential System with Non-instantaneous Impluleses and State Dependent Delay

• Aziz Khan ^[1] ; Qura Tul Ain ^[2] ; Thabet Abdeljawad ^[4] ; Kottakkaran Sooppy Nisar ^[3]
  1. [1] Prince Sultan University

     Prince Sultan University

     Arabia Saudí

     
  2. [2] Guizhou University

     Guizhou University

     China

     
  3. [3] Prince Sattam Bin Abdulaziz University

     Prince Sattam Bin Abdulaziz University

     Arabia Saudí

     
  4. [4] Prince Sultan University & China Medical University

  Mostrar afiliaciones +
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this article, we discuss the exact controllability of a fractional order differential system involving Hilfer fractional(HF) derivative, state-dependent delay function and impulsive conditions. To obtain the proposed result, we use the semigroup theory, theory of measure of non-compactness and fixed point technique. Finally, an example is given to illustrate the application of the obtained results.

• Referencias bibliográficas
  • 1. Khan, H., Chen, W., Khan, A., Khan, T.S., Al-Madlal, Q.M.: Hyers–Ulam stability and existence criteria for coupled fractional differential...
  • 2. Khan, H., Tunc, C., Khan, A.: Green function’s properties and existence theorems for nonlinear singulardelay-fractional differential equations....
  • 3. Shah, K., Khan, Z.A., Ali, A., Amin, R., Khan, H., Khan, A.: Haar wavelet collocation approach for the solution of fractional order COVID-19...
  • 4. Devi, A., Kumar, A., Abdeljawad, T., Khan, A.: Stability analysis of solutions and existence theory of fractional Langevin equation. Alex....
  • 5. Devi, A., Kumar, A.: Existence of solutions for fractional Langevin equation involving generalized Caputo derivative with periodic boundary...
  • 6. Devi, A., Kumar, A., Abdeljawad, T., Khan, A.: Existence and stability analysis of solutions for fractional Langevin equation with nonlocal...
  • 7. Devi, A., Kumar, A., Baleanu, D., Khan, A.: On stability analysis and existence of positive solutions for a general non-linear fractional...
  • 8. Devi, A., Kumar, A.: Hyers–Ulam stability and existence of solution for hybrid fractional differential equation with p-Laplacian operator....
  • 9. Bedi, P., Kumar, A., Abdeljawad, T., & Khan, A. (2020). S-asymptotically ω-periodic mild solutions and stability analysis of Hilfer...
  • 10. Bedi, P., Kumar, A., Abdeljawad, T., Khan, A., Gomez-Aguilar, J.F.: Mild solutions of coupled hybrid fractional order system with Caputo–Hadamard...
  • 11. Kumar, A., & Bedi, P., On the Mild Solutions of Impulsive Semilinear Fractional Evolution Equations. In Proceedings of International...
  • 12. Bedi, P., Khan, A., Kumar, A., Abdeljawad, T.: Computational study of fractional order vector borne diseases model. Fractals (2022). https://doi.org/10.1142/S0218348X22401491
  • 13. Podlubny, I.: Fractional Differential Equations, vol. 198. Academic Press, San Diego (1998). https:// doi.org/10.2307/2653160
  • 14. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, vol. 204. Elsevier, New...
  • 15. Sher, M., Shah, K., Khan, Z.A., Khan, H., Khan, A.: Computational and theoretical modeling of the transmission dynamics of novel COVID-19...
  • 16. Khan, A., Alshehri, H.M., Abdeljawad, T., Al-Mdallal, Q.M., Khan, H.: Stability analysis of fractional nabla difference COVID-19 model....
  • 17. Gomez-Aguilar, J.F., Cordova-Fraga, T., Abdeljawad, T., Khan, A., Khan, H.: Analysis of fractalfractional malaria transmission model....
  • 18. Boudjerida, A., Seba, D.: Controllability of nonlocal Hilfer fractional delay dynamic inclusions with non-instantaneous impulses and non-dense...
  • 19. Elshenhab, A.M., Wang, X.T.: Controllability and Hyers–Ulam stability of differential systems with pure delay. Mathematics 10(8), 1248...
  • 20. Sundaravadivoo, B.: Controllability analysis of nonlinear fractional order differential systems with state delay and non-instantaneous...
  • 21. Muslim, M., Kumar, A.: Controllability of fractional differential equation of order α ∈ (1, 2] with non-instantaneous impulses. Asian...
  • 22. Bedi, P., Kumar, A., Abdeljawad, T., Khan, A.: Study of Hilfer fractional evolution equations by the properties of controllability and...
  • 23. Bedi, P., Kumar, A., Abdeljawad, T., Khan, Z.A., Khan, A.: Existence and approximate controllability of Hilfer fractional evolution equations...
  • 24. Bedi, P., Kumar, A., Khan, A.: Controllability of neutral impulsive fractional differential equations with Atangana–Baleanu–Caputo derivatives....
  • 25. Aimene, D., Baleanu, D., Seba, D.: Controllability of semilinear impulsive Atangana–Baleanu fractional differential equations with delay....
  • 26. Heping, M.A., Biu, L.I.U.: Exact controllability and continuous dependence of fractional neutral integro-differential equations with state-dependent...
  • 27. Cheng, Y., Agarwal, R.P., Regan, D.O.: Existence and controllability for nonlinear fractional differential inclusions with nonlocal boundary...
  • 28. Singh, V.: Controllability of Hilfer fractional differential systems with non-dense domain. Numer. Funct. Anal. Optim. 40(13), 1572–1592...
  • 29. Bedi, P., Kumar, A., Abdeljawad, T., Khan, A.: Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations....
  • 30. Hale, J.K., Kato, J.: Phase space for retarded equations with infinite delay. Funk Ekvac 21(1), 11–41 (1978)
  • 31. Banas, J.: On measures of noncompactness in Banach spaces. Comment. Math. Univ. Carol. 21(1), 131–143 (1980)
  • 32. Sousa, J.V.D.C., Jarad, F., Abdeljawad, T.: Existence of mild solutions to Hilfer fractional evolution equations in Banach space. Ann....