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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Conformable Impulsive Delay Differential Equations

Journal of Applied Nonlinear Dynamics 13(1) (2024) 177--189 | DOI:10.5890/JAND.2024.03.012

Madhuri Sunkavilli, G.V.S.R. Deekshitulu

Department of Mathematics, UCEK, JNTUK, Kakinada, A.P., India

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Abstract

References

  1. [1]  Kilbas, A.A, Srivastava, M.H. and Trujillo, J.J. (2006), Theory and applications of fractional differential equations, 204, elsevier.
  2. [2] Miller, K.S. and Ross B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York.
  3. [3] Podlubny I. (1999), Fractional Differential Equations, Academic Press, San Diego.
  4. [4] Khan, Z.A., Ahmad, I., and Shah, K. (2021), Applications of fixed point theory to investigate a system of fractional order differential equations, Journal of Function Spaces, 2021, Article ID 1399764.
  5. [5]  Khalil, R., Al Horani, M., Yousef, A., and Sababheh, M. (2014), A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70.
  6. [6]  Ali, A., Shah, K., Abdeljawad, T., Mahariq, I., and Rashdan, M. (2021), Mathematical analysis of nonlinear integral boundary value problemma of proportional delay implicit fractional differential equations with impulsive conditions, Bound Value Problemmas, 2021(7), 1-27.
  7. [7] Iyiola, O.S. and Nwaeze, E.R. (2016), Some new results on the new conformable fractional calculus with application using D'Alambert approach, Progress in Fractional Differentiation and Applications, 2(2), 115-122.
  8. [8] Li, M., Wang, J., and O'Regan, D. (2019), Existence and Ulam's stability for conformable fractional differential equations with constant coefficients, Bulletin of the Malaysian Mathematical Sciences Society, 42(4), 1791-1812.
  9. [9] Tariboon, J. and Ntouyas, S.K. (2016), Oscillation of impulsive conformable fractional differential equations, Open Mathematics, 14(1), 497-508.
  10. [10] Bainov, D.D. and Dishliev, A.B. (1990), Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population, Applied Mathematics and Computation, 39(1), 37-48.
  11. [11] Choisy, M., Guégan, J.F., and Rohani, P. (2006), Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects, Physica D: Nonlinear Phenomena, 223(1), 26-35.
  12. [12] d'Onofrio, A. (2005), On pulse vaccination strategy in the SIR epidemic model with vertical transmission, Applied Mathematics Letters, 18(7), 729-732.
  13. [13] Bainov, D.D. and Simeonov, P.S. (1993), Impulsive Differential Equations: Periodic Solutions and Applications, 66, CRC Press.
  14. [14] Benchohra, M., Henderson, J., and Ntouyas, S.K. (2006), Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, New York, 2.
  15. [15]  Khan, Z. A., Gul, R., and Shah, K. (2021), On impulsive boundary value problemma with Riemann-Liouville fractional order derivative, Journal of Function Spaces, 2021, 1-11.
  16. [16]  Shah, K., Ahmad, I., Nieto, J.J., Rahman, G.U., and Abdeljawad, T. (2022), Qualitative investigation of nonlinear fractional coupled pantograph impulsive differential equations, Qualitative Theory of Dynamical Systems, 21(131), 131.
  17. [17] You, Z. and Wang, J. (2018), Stability of impulsive delay differential equations, Journal of Applied Mathematics and Computing, 56(1), 253-268.
  18. [18] Mahmudov, N.I. and Aydın, M. (2021), Representation of solutions of nonhomogeneous conformable fractional delay differential equations, Chaos, Solitons $\&$ Fractals, 150, 111190.
  19. [19] Abdelhakim, A.A. and Machado, J.A.T. (2019), A critical analysis of the conformable derivative, Nonlinear Dynamics, 95(4), 3063-3073.
  20. [20]  Abdeljawad, T. (2015), On conformable fractional calculus, Journal of computational and Applied Mathematics, 279, 57-66.
  21. [21]  Xiao, G. and Wang, J. (2021), Representation of solutions of linear conformable delay differential equations, Applied Mathematics Letters, 117, 107088.
  22. [22] Smart, D.R. (1980), Fixed Point Theorems, Cambridge University Press, Cambridge, 66.

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