KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 47 Issue: 5

Hyers-Ulam stability of first-order non-linear delay differential equations with fractional integrable impulses

Akbar Zada(DEPARTMENT OF MATHEMATICS, UNIVERSITY OF PESHAWAR)
Syed Omar Shah(DEPARTMENT OF MATHEMATICS, UNIVERSITY OF PESHAWAR)
Sayfa
—
Yayın Tarihi
2018-10-16
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Our approach uses abstract Grönwall lemma together with integral inequality of Grönwall type for piecewise continuous

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of first-order non-linear delay differential equations with fractional integrable impulses.
📊
Temel Bulgular & Veri:This paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of first-order non-linear delay differential equations with fractional integrable impulses.
💡
Sonuç & Katkı:Our approach uses abstract Grönwall lemma together with integral inequality of Grönwall type for piecewise continuous
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hyers-Ulam stability · Hyers-Ulam-Rassias stability · fractional integrable impulses

Abstract

This paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of first-order non-linear delay differential equations with fractional integrable impulses. Our approach uses abstract Grönwall lemma together with integral inequality of Grönwall type for piecewise continuous

🔖

Bu Makaleye Atıf Yap

Zada, A., Shah, S. O. (2018). Hyers-Ulam stability of first-order non-linear delay differential equations with fractional integrable impulses. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 5. https://ajindex.com/articles/1402888

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (43)

  1. Bainov, D. D. and Dishliev, A., Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population, Comp. Rend. Bulg. Scie. 42(6), 29-32, 1989.
  2. Bainov, D. D. and Simenov, P. S., Systems with impulse effect stability theory and applica- tions, Ellis Horwood Limited, Chichester 1989.
  3. Brzdek, J. and Eghbali, N., On approximate solutions of some delayed fractional differential equations, Appl. Math. Lett. 54, 31-35, 2016.
  4. Dishliev, A. and Bainov, D. D., Dependence upon initial conditions and parameters of solutions of impulsive differential equations with variable structure, Int. J. Theor. Phys. 29(6), 655-676, 1990.
  5. Gowrisankar, M., Mohankumar, P. and Vinodkumar, A., Stability results of random im- pulsive semilinear differential equations, Acta Math. Sci. 34(4), 1055-1071, 2014.
  6. Huang, J., Alqifiary, Q. H. and Li, Y., Superstability of differential equations with boundary conditions, Elec. J. Diff. Eq. 2014(215), 1-8, 2014.
  7. Huang, J., Jung, S.-M. and Li, Y., On the Hyers-Ulam stability of non-linear differential equations, Bull. Korean Math. Soc. 52(2), 685-697, 2015.
  8. Huang, J. and Li, Y., Hyers-Ulam stability of linear functional differential equations, J. Math. Anal. Appl. 426, 1192-1200, 2015.
  9. Huang, J. and Li, Y., Hyers-Ulam stability of delay differential equations of first order, Math. Nachr. 289(1), 60-66, 2016.
  10. Hyers, D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27(4), 222-224, 1941.
  11. Jung, S.-M., Hyers-Ulam stability of linear differential equations of first order. III, J. Math. Anal. Appl. 311, 139-146, 2005.
  12. Jung, S.-M., Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer Optim. Appl., Springer, NewYork 48, 2011.
  13. Li, Y. and Shen, Y., Hyers-Ulam stability of nonhomogeneous linear differential equations of second order, Internat. J. Math. Math. Sci. 2009.
  14. Li, Y. and Shen, Y., Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett. 23, 306-309, 2010.
  15. Li, T. and Zada, A., Connections between Hyers-Ulam stability and uniform exponential stability of discrete evolution families of bounded linear operators over Banach spaces, Adv. Difference Equ. 153, 2016.
  16. Li, T., Zada, A. and Faisal, S., Hyers-Ulam stability of nth order linear differential equa- tions, J. Nonlinear Sci. Appl. 9, 2070-2075, 2016.
  17. Liao, Y. and Wang, J., A note on stability of impulsive differential equations, Bound. Val. Prob. 67, 2014.
  18. Lupulescu, V. and Zada, A., Linear impulsive dynamic systems on time scales, Electron. J. Qual. Theory Diff. Equ. 11, 1-30, 2010.
  19. Miura, T., Miyajima, S. and Takahasi, S. E., A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl. 286, 136-146, 2003.
  20. Nenov, S., Impulsive controllability and optimization problems in population dynamics, Nonl. Anal. 36, 881-890, 1999.
  21. Obloza, M., Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat. 259-270, 1993.
  22. Obloza, M., Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat. 14, 141-146, 1997.
  23. Parthasarathy, C., Existence and Hyers-Ulam Stability of nonlinear impulsive differential equations with nonlocal conditions, Elect. Jour. Math. Ana. and Appl. 4(1), 106-117, 2016.
  24. Popa, D. and Rasa, I., Hyers-Ulam stability of the linear differential operator with noncon- stant coefficients, Appl. Math. Comp. 219, 1562-1568, 2012.
  25. Rassias, T. M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, 297-300, 1978.
  26. Rezaei, H., Jung, S. -M. and Rassias, T. M., Laplace transform and Hyers-Ulam stability of linear differential equations, J. Math. Anal. Appl. 403, 244-251, 2013.
  27. Rus, I. A., Gronwall lemmas: ten open problems, Sci. Math. Jpn. 70, 221-228, 2009.
  28. Samoilenko, A. M. and Perestyuk, N. A., Stability of solutions of differential equations with impulse effect, Differ. Equ. 13, 1981-1992, 1977.
  29. Shah, R. and Zada, A., A fixed point approach to the stability of a nonlinear volterra integrodifferential equations with delay, Hacet. J. Math. Stat. 2017, 47 (3), 615-623, 2018.
  30. Tang, S., Zada, A., Faisal, S., El-Sheikh, M. M. A. and Li, T., Stability of higher-order nonlinear impulsive differential equations, J. Nonlinear Sci. Appl. 9, 4713-4721, 2016.
  31. Ulam, S. M., A collection of the mathematical problems, Interscience, New York, 1960.
  32. Wang, J., Feckan, M. and Zhou, Y., Ulam's type stability of impulsive ordinary differential equations, J. Math. Anal. Appl. 395, 258-264, 2012.
  33. Wang, J., Feckan, M. and Zhou, Y., On the stability of first order impulsive evolution equations, Opuscula Math. 34, 639-657, 2014.
  34. Wang, C. and Xu, T. Z., Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives, Appl. Math. 60(4), 383-393, 2015.
  35. Wang, J. and Zhang, Y., A class of nonlinear differential equations with fractional integrable impulses, Com. Nonl. Sci. Num. Sim. 19, 3001-3010, 2014.
  36. Xu, B. and Brzdek, J., Hyers-Ulam stability of a system of first order linear recurrences with constant coefficients, Discrete Dyn. Nat. Soc. 5 pages, 2015.
  37. Xu, B., Brzdek, J. and Zhang, W., Fixed point results and the Hyers-Ulam stability of linear equations of higher orders, Pacific J. Math. 273(2), 2015, 483-498.
  38. Zada, A., Ali, W. and Farina, S., Hyers-Ulam stability of nonlinear differential equations with fractional integrable impulses, Math. Methods Appl. Sci., 40, 5502-5514, 2017.
  39. Zada, A., Faisal, S. and Li, Y., On the Hyers-Ulam stability of first-order impulsive delay differential equations, J. Funct. Spaces, 6 pages, 2016.
  40. Zada, A., Faisal, S. and Li, Y., Hyers-Ulam-Rassias stability of non-linear delay differential equations, J. Nonlinear Sci. Appl. 10, 504-510, 2017.
  41. Zada, A., Khan, F. U., Riaz, U. and Li, T., Hyers-Ulam stability of linear summation equations, Punjab U. J. Math. 49(1), 19-24, 2017.
  42. Zada, A., Shah, O. and Shah, R., Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems, Appl. Math. Comput. 271, 512-518, 2015.
  43. Zada, A., Faisal, S. and Li, Y., On the Hyers-Ulam stability of first-order impulsive delay differential equations, J. Funct. Spaces, 6 pages, 2016.