Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 1

Ulam-Hyers-Stability for nonlinear fractional neutral differential equations

Sayfa
157–169
Yayın Tarihi
2022-10-18
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)

An example is also given to show the applicability of our results.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We discuss Ulam-Hyers stability, Ulam-Hyers-Rassias stability and Generalized UlamHyers-Rassias stability for a class of nonlinear fractional functional differential equations with delay involving Caputo fractional derivative by using Picard operator.
📊
Temel Bulgular & Veri:We discuss Ulam-Hyers stability, Ulam-Hyers-Rassias stability and Generalized UlamHyers-Rassias stability for a class of nonlinear fractional functional differential equations with delay involving Caputo fractional derivative by using Picard operator.
💡
Sonuç & Katkı:An example is also given to show the applicability of our results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

We discuss Ulam-Hyers stability, Ulam-Hyers-Rassias stability and Generalized UlamHyers-Rassias stability for a class of nonlinear fractional functional differential equations with delay involving Caputo fractional derivative by using Picard operator. An example is also given to show the applicability of our results.

🔖

Bu Makaleye Atıf Yap

NİAZİ, A. U. K., WEİ, J., REHMAN, M. U., JUN, D. (2022). Ulam-Hyers-Stability for nonlinear fractional neutral differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 157–169. https://ajindex.com/articles/529731

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. L. Chen, Y. He, Y. Chai and R. Wu, New results on stability and stabilization of a class of nonlinear fractional-order systems, Nonlinear Dyn. 75 (4), 633–641, 2014.
  2. L. Chen, C. Liu, R. Wu, Y. He and Y. Chai, Finite-time stability criteria for a class of fractional-order neural networks with delay, Neural Comput. Appl. 27 (3), 549–556, 2016.
  3. L. Chen, R. Wu, J. Cao and J.B. Liu, Stability and synchronization of memristor-based fractional-order delayed neural networks, Neural Netw., 71, 37–44, 2015.
  4. L. Chen, R. Wu, Z. Chu and Y. He, Stabilization of fractional-order coupled systems with time delay on networks, Nonlinear Dyn. 88 (1), 521–528, 2017.
  5. K. Diethelm and A.D. Freed, On the solution of nonlinear fractional-order di erential equations used in the modeling of viscoplasticity, in: Scientific Computing in Chemical Engineering II, 217–224,
  6. Springer, Berlin, Heidelberg, 1999.
  7. A.M. El-Sayed, Fractional-order di usion-wave equation, Internat. J. Theoret. Phys. 35 (2), 311–322, 1996.
  8. W.G. Glockle and T.F. Nonnenmacher, A fractional calculus approach to self-similar protein dynamics, Biophys. J. 68 (1), 46–53, (1995). R. Hilfer, ed., Applications of fractional calculus in physics, World Scientific, 2000.
  9. D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (4), 222–224, 1941.
  10. D.H. Hyers, G. Isac and T.M. Rassias, Stability of functional equations in several variables, Birkhuser Boston. Inc., Boston, MA, 1998.
  11. S.M. Jung, Hyers-Ulam-Rassias stability of functional equations in mathematical analysis, Hadronic Press, 2001.
  12. S.M. Jung, Hyers-Ulam stability of linear di erential equations of first order, Appl. Math. Lett. 17 (10), 1135–1140, 2004.
  13. S. Jung, A fixed point approach to the stability of di erential equations y0 = F (x, y), Bull. Malays. Math. Sci. Soc. 33, 47–56, 2010.
  14. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Di erential Equations, North-Holland Mathematics Studies, 204, 2006.
  15. X. Li, S. Liu and W. Jiang, Positive solutions for boundary value problem of nonlinear fractional functional di erential equations, Appl. Math. Comput. 217 (22), 9278– 9285, 2011.
  16. S. Liu, X. Li, X.F. Zhou and W. Jiang, Synchronization analysis of singular dynamical networks with unbounded time-delays, Adv. Difference Equ. 193, 1–9, 2015.
  17. K.S. Miller and B. Ross, An introduction to the fractional calculus and fractional di erential equations, Mathematics in Science and Engineering 198, 1993. T. Miura