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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 4

Ulam stability results for the solutions of nonlinear implicit fractional order differential equations

Zeeshan Ali
Akbar Zada
Kamal Shah
Pages
1092–1109
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The main results are illustrated by providing a couple of examples

📌 3 Key Takeaways

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Objective & Hypothesis:In this manuscript, we study the existence and uniqueness of solution for a class of fractional order boundary value problem (FBVP) for implicit fractional differential equations with Riemann-Liouville derivative.
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Key Findings & Data:Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the proposed problem.
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Conclusion & Impact:The main results are illustrated by providing a couple of examples
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riemann-Liouville fractional derivative · implicit fractional differential equations · existence

Abstract

In this manuscript, we study the existence and uniqueness of solution for a class of fractional order boundary value problem (FBVP) for implicit fractional differential equations with Riemann-Liouville derivative. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the proposed problem. The concerned analysis is carried out through using classical technique of nonlinear functional analysis. The main results are illustrated by providing a couple of examples

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Cite This Article

Ali, Z., Zada, A., Shah, K. (2022). Ulam stability results for the solutions of nonlinear implicit fractional order differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1092–1109. https://ajindex.com/articles/530131

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References (18)

  1. B. Ahmad and J.J. Nieto, Riemann–Laiouville fractional differential equations with fractional boundary conditions, Fixed Point Theor, 13 (2), 329–336, 2012
  2. B. Ahmad and S. Sivasundaram, On four–point nonlocal boundary value problems of nonlinear integro–differential equations of fractional order, Appl. Math. Comput. 217, 480–487, 2010
  3. N. Ahmad, Z. Ali, K. Shah, A. Zada and G. Ur Rahman, Analysis of implicit type nonlinear dynamical problem of impulsive fractional differential equations, Complexity, 2018, 1–15, 2018
  4. Z. Ali, A. Zada and K. Shah, Existence and stability analysis of three point boundary value problem, Int. J. Appl. Comput. Math. 2017, DOI:10.1007/s40819–017–0375–8
  5. G.A. Anastassiou, On right fractional calculus, Chaos Solitons Fractals, 42 (1), 365– 376, 2009
  6. D. Baleanu, Z.B. Güvenc and J.A.T. Machado, New Trends in Nanotechnology and Fractional Calculus Applications, Springer, New York, 2010
  7. M. Benchohra and S. Bouriah, Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order, Moroccan J. Pure Appl. Anal. 1 (1), 22–37, 2015
  8. M. Benchohra, S. Hamani and S.K. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Anal. 71, 2391– 2396, 2009
  9. A. Browder, Mathematical Analysis: An Introduction, New York, Springer-Verlag, 1996
  10. M. El-Shahed and J.J. Nieto, Nontrivial solutions for a nonlinear multi–point boundary value problem of fractional order, Comput. Math. Appl. 59, 3438–3443, 2010
  11. A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003
  12. E. Hiffer (ed.), Application of Fractional Calculus in Physics, Word Scientific, Singapore, 2000
  13. D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A, 27 (4), 222–224, 1941
  14. D.H. Hyers, G. Isac and T.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäiuser, Boston, 1998
  15. J.K. Hale and S.M.V. Lunel, Introduction to Functional Differential Equations, in: Applied Mathematicals Sciences series, Springer–Verlag, New York, 99, 1993
  16. R.W. Ibrahim, Generalized Ulam–Hyers stability for fractional differential equations, Int. J. Math. 23 (5), 9 pages, 2012
  17. S.M. Jung, Hyers–Ulam stability of linear differential equations of first order, Appl. Math. Lett. 19, 854–858, 2006
  18. R.A. Khan and K. Shah, K. Existence and uniquenes