SavedAdd your journal

Journals / Proceedings of International Mathematical Sciences / 2022 / Volume: 4 Issue: 2

Some results on the study of -Hilfer type fuzzy fractional differential equations with time delay

R. Vivek(Sri Ramakrishna Mission Vidyalaya College of Arts and Science)0000-0002-1451-0875
D. Vivek Vivek(PSG College of Arts and Science)0000-0003-0951-8060
Kangarajan K.(Sri Ramakrishna Mission Vidyalaya College of Arts and Science)0000-0001-5556-2658
Elsayed Elsayed(King Abdulaziz University)0000-0003-0894-8472
Pages
—
Publication Date
2022-12-31
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

By applying standard theorems and a hypothetical condition, we explore the existence of solution and stabilty results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper is concerned with the finite-time stability of -Hilfer type fuzzy fractional differential equations (FFDEs) with time delay.
📊
Key Findings & Data:This paper is concerned with the finite-time stability of -Hilfer type fuzzy fractional differential equations (FFDEs) with time delay.
💡
Conclusion & Impact:By applying standard theorems and a hypothetical condition, we explore the existence of solution and stabilty results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fuzzy differential equations · Finite-time stability · Existence

Abstract

This paper is concerned with the finite-time stability of -Hilfer type fuzzy fractional differential equations (FFDEs) with time delay. By applying standard theorems and a hypothetical condition, we explore the existence of solution and stabilty results.

🔖

Cite This Article

Vivek, R., Vivek, D. V., K., K., Elsayed, E. (2022). Some results on the study of -Hilfer type fuzzy fractional differential equations with time delay. Proceedings of International Mathematical Sciences, Volume: 4 Issue: 2. https://doi.org/10.47086/pims.1168552

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (35)

  1. O.P. Agrawal, Some generalized fractional calculus operators and their applications in integral equations, Fract. Calc. Appl. Anal., 15(2012), 700-711.
  2. B. Ahmad, J.J. Nieto, Riemann-Liouville fractional differential equations with fractional boundary conditions, Fixed Point Theory, 13(2013), 329-336.
  3. K. Balachandran, S. Kiruthika, J. Trujillo, Existence of solutions of nonlinear fractional pantograph equations, Acta Mathematica Scientia., 3(33)(2013), 712-720.
  4. X.K. Cao, J.R. Wang, Finite-time stability of a class of oscillating systems with two delays, Math. Methods Appl. Sci., 41(13)(2018), 4943-4954.
  5. F.F. Du, J.G. Lu, Finite-time stability of fractional-order fuzzy cellular neural networks with time-delays, Fuzzy Set. Syst., 438(2022), 107-120.
  6. O.S. Fard, M. Salehi, A survey on fuzzy fractional variational problems, J. Comput. Appl. Math., 271(2014), 71-82.
  7. K.M. Furati, N.D. Kassim, N.E. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl., 64(2012), 1616-1626.
  8. A. Granas, J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
  9. R. Hilfer, Applications of Fractional Calculus in Physics, Singapore: World Scientific, 2000.
  10. N.V. Hoa, H. Vu, T.M. Duc, Fuzzy fractional differential equations under Caputo- Katugampola fractional derivative approach, Fuzzy Set. Syst., 375(2019), 70-99.
  11. Y. Jiang, J. Qiu, F. Meng, Existence and finite-time stability results of fuzzy Hilfer-Katugampola fractional delay differential equations 1, J. Intell. Fuzzy Syst., 2022, 1-10.
  12. K. Kanagarajan, R. Vivek, D. Vivek, E.M. Elsayed, Existence Results for Fuzzy Differential Equations with Hilfer Fractional Derivative, Ann. Commun. Math., 5(1)(2022), 38-54.
  13. U.N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6(4)(2014), 1-15.
  14. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, Elsevier, Amsterdam, 207, 2006.
  15. K. Kotsamran, W. Sudsutad, C. Thaiprayoon, J. Kongson, Analysis of a nonlinear Hilfer fractional integrodifferential equation describing cantilever beam model with nonlinear boundary conditions, Fractal. Fract., 5(177), 2021.
  16. M.M. Li, J.R. Wang, Finite-time stability and relative controllability of Riemann-Liouville fractional delay differential equations, Math. Methods Appl. Sci., 42(18)(2019), 6607-6623.
  17. Q. Li, D.F. Luo, Z.G. Luo, Q.X. Zhu, On the novel finite-time stability results for uncertain fractional delay differential equations involving noninstantaneous impulses, Math. Probl. Eng., 9097135(2019), 2019.
  18. H.V. Long, N.T.K. Son, N.V. Hoa, Fuzzy fractional partial differential equations in partially ordered metric spaces, Iran. J. Fuzzy Syst., 14(2017), 107-126.
  19. H.V. Long, N.P. Dong, An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncer tainty, Fixed Point Theory Appl., 20(2018), 37.
  20. D.F. Luo, Z.G. Luo, Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses, Math. Slovaca., 70(5)(2020), 1231-48.
  21. S.K. Ntouyas, A survey on existence results for boundary value problems of Hilfer fractional differential equations and inclusions, Foundations., 1(2021), 63-98.
  22. E.C. Oliveira, J.A.T. Machado, A Riew of Definitions for Fractional Derivatives and Integral, Math. Probl. Eng., 2014(238)(459), 2014.
  23. D.S. Oliveira, E.C. Oliveira, Hilfer-Katugampola fractional derivative, Comput. Appl. Math., 37(2018), 3672-3690.
  24. I. Podlubny, Fractional differential equations, Acadamic Press, San Diego, 1999.
  25. C. Promsakon, S.K. Ntouyas, J. Tariboon, Hilfer-Hadamard nonlocal integro multipoint fractional boundary value problems, J. Funct. Spaces., 2021(9)(8031524), 2021.
  26. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives Theory and Applications, New York: Gordon and Breach, 1993.
  27. K. Shah, A. Ali, S. Bushnaq, Hyers-Ulam stability analysis to implicit Cauchy problem of fractional differential equations with impulsive conditions, Math. Methods Appl. ci., 41(17)(2018), 8329-8343.
  28. L. Stefanini, B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal. Theor., 71(2009), 1311-1328.
  29. J.V.C. Sousa, E.C. Oliveira, On the -Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., 60(2018), 72-91.
  30. J.V.C. Sousa, E.C. Oliveira, On the Ulam-Hyers-Rassias stability for nonlinear fractional differential equations using the -Hilfer operator, J. Fixed Point Theory Appl., 20(2018), 1-21.
  31. D. Vivek, K. Kanagarajan, E.M. Elsayed, Some existence and stability results for Hilfer-fractional implicit differential equations with nonlocal conditions, Mediterr. J. Math., 15(2018), 1-15.
  32. D. Vivek, K. Kanagarajan, S. Sivasundaram, Dynamics and stability of pantograph equations via hilfer fractional derivative, Nonlinear Studies., 23(4)(2016), 685-698.
  33. R. Vivek, E.M. Elsayed, K. Kanagarajan, D. Vivek, Qualitative Analysis of Quaternion Fuzzy Fractional Differential Equations with -Hilfer Fractional Derivative, Pure. Appl. Anal., 6(2022), 2022.
  34. H. Vu, N.V. Hoa, Hyers-ulam stability of fuzzy fractional volterra integral equations with the kernal functions via successive approximation method, Fuzzy set syst., 419(2021), 67-98.
  35. J.Wang, Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Appl. Math. Comput., 2015(266), 850-859.