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Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses

Yıl 2023, , 115 - 127, 17.09.2023

Ravichandran Vıvek Kangarajan K. , Dvivek Vivek , Elsayed Elsayed

https://doi.org/10.33434/cams.1257750
Cited By: 1

Öz

This paper deals with the existence, uniqueness, and Ulam-stability outcomes for $\Xi$-Hilfer fractional fuzzy differential equations with impulse. Further, by using the techniques of nonlinear functional analysis, we study the Ulam-Hyers-Rassias stability.

Anahtar Kelimeler

Existence Fuzzy impulsive differential equation $\Xi$-Hilfer fractional derivative Uniqueness Ulam-Hyers-Rassias stability

Destekleyen Kurum

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Proje Numarası

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Teşekkür

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Kaynakça

  • [1] M. Benchohra, J.J. Nieto, A. Ouahab, Fuzzy solutions for impulsive differential equations, Commun. Appl. Anal., 11(2007), 379-394.
  • [2] M. Benchohra, J. Henderson, S.L. Ntouyas, Impulsive Differential Equations and Inclusions, New York, Hindawi Publishing Corporation, 2(2006).
  • [3] M. Feckan, Y. Zhou, J. Wang, On the concept and existence of solutions for impulsive fractional differential equations, Commun. Nonlinear. Sci. Numer. Simul., 17(7)(2012), 3050-3060.
  • [4] T.L. Guo, W. Jiang, Impulsive fractional functional differential equations, Comput. Math. Appl., 64(2012), 3414-3424.
  • [5] N.V. Hoa, D. O’Regan, A remark on y-Hilfer fractional differential equations with non-instantaneous impulses, Math. Methods. Appl. Sci., 43(2020), 3354-3368.
  • [6] N.V. Hoa, T.V. An, Fuzzy differential equations with Riemann-Liouville generalized fractional integrable impulses, Fuzzy Sets Syst., 2021.
  • [7] D. Luo, Z. 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), 1231-1248.
  • [8] J.V.D.C. Sousa, K.D. Kucche, E.C. de Oliveira, Stability of y-Hilfer impulsive fractional differential equations, Appl. Math. Lett., 88(2019), 73-80.
  • [9] J.V.D.C. Sousa, D.D.S. Oliveira, E.C. de Oliveira, On the existence and stability for non-instantaneous impulsive fractional integro-differential equations, Math. Methods. Appl. Sci., 42(2019), 1249-1261.
  • [10] K.M. Furati, M.D. Kassim, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl., 64(6)(2012), 1616-1626.
  • [11] R. Hilfer, Applications of Fractional Calculus in Physics, Singapore, World scientific, 2000.
  • [12] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006.
  • [13] I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999.
  • [14] J.V.D.C. Sousa, E.C. de Oliveira, On the y-Hilfer fractional derivative, Commun. Nonlinear. Sci. Numer. Simul., 60(2018), 72-91.
  • [15] B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy sets syst., 230(2013), 119-141.
  • [16] V. Lakshikantham, R.N. Mohapatra, Theory of fuzzy differential equations and applications, London, CRC Press, 2003.
  • [17] L. Sajedi, N. Eghbali, H. Aydi, Impulsive coupled system of fractional differential equations with Caputo-Katugampola fuzzy fractional derivative, Hindawi. J. Math., 13(2021).
  • [18] X. Chen, H. Gu, X. Wang, Existence and uniqueness for fuzzy differential equation with Hilfer-Katugampola fractional derivative, Adv. Differ. Equ., 2020(2020), 241.
  • [19] N.V. Hoa, H. Vu, T.M. Duc, Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach, Fuzzy Sets Syst., 375(2019), 70-99.
  • [20] N.V. Hoa, Fuzzy fractional functional differential equations under Caputo gH-differentiability, Commun. Nonlinear. Sci. Numer. Simul., 22(1-3)(2015), 1134-1157.
  • [21] D.F. Luo, T. Abdeljawad, Z.G. Luo, Ulam-Hyers stability results for a novel nonlinear nabla caputo fractional variable order difference system, Turk. J. Math., 45(1)(2021), 456-70.
  • [22] D. Luo, K. Shah, Z. Luo, On the novel Ulam-Hyers stability for a class of nonlinear y-Hilfer fractional differential equation with time-varying delays, Mediterr. J. Math., 16(5)(2019), 112.
  • [23] S. Rashid, F. Jarad, K.M. Abualnaja, On fuzzy Volterra-Fredholm integrodifferential equation associated with Hilfergeneralized proportional fractional derivative, AIMS Math., 6(2021), 10920-10946.
  • [24] H. Vu, J.M. Rassias, N.V. Hoa, Ulam-Hyers-Rassias stability for fuzzy fractional integral equations, Iran. J. Fuzzy syst., 17(2020), 17-27.
  • [25] X. Wang, D. Luo, Q. Zhu, Ulam-Hyers stability of Caputo type fuzzy fractional differential equation with time-delays, Chaos. Solitons. Fractals., 156(2022), 111822.

Yıl 2023, , 115 - 127, 17.09.2023

Ravichandran Vıvek Kangarajan K. , Dvivek Vivek , Elsayed Elsayed

https://doi.org/10.33434/cams.1257750
Cited By: 1

Öz

Proje Numarası

-

Kaynakça

  • [1] M. Benchohra, J.J. Nieto, A. Ouahab, Fuzzy solutions for impulsive differential equations, Commun. Appl. Anal., 11(2007), 379-394.
  • [2] M. Benchohra, J. Henderson, S.L. Ntouyas, Impulsive Differential Equations and Inclusions, New York, Hindawi Publishing Corporation, 2(2006).
  • [3] M. Feckan, Y. Zhou, J. Wang, On the concept and existence of solutions for impulsive fractional differential equations, Commun. Nonlinear. Sci. Numer. Simul., 17(7)(2012), 3050-3060.
  • [4] T.L. Guo, W. Jiang, Impulsive fractional functional differential equations, Comput. Math. Appl., 64(2012), 3414-3424.
  • [5] N.V. Hoa, D. O’Regan, A remark on y-Hilfer fractional differential equations with non-instantaneous impulses, Math. Methods. Appl. Sci., 43(2020), 3354-3368.
  • [6] N.V. Hoa, T.V. An, Fuzzy differential equations with Riemann-Liouville generalized fractional integrable impulses, Fuzzy Sets Syst., 2021.
  • [7] D. Luo, Z. 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), 1231-1248.
  • [8] J.V.D.C. Sousa, K.D. Kucche, E.C. de Oliveira, Stability of y-Hilfer impulsive fractional differential equations, Appl. Math. Lett., 88(2019), 73-80.
  • [9] J.V.D.C. Sousa, D.D.S. Oliveira, E.C. de Oliveira, On the existence and stability for non-instantaneous impulsive fractional integro-differential equations, Math. Methods. Appl. Sci., 42(2019), 1249-1261.
  • [10] K.M. Furati, M.D. Kassim, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl., 64(6)(2012), 1616-1626.
  • [11] R. Hilfer, Applications of Fractional Calculus in Physics, Singapore, World scientific, 2000.
  • [12] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006.
  • [13] I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999.
  • [14] J.V.D.C. Sousa, E.C. de Oliveira, On the y-Hilfer fractional derivative, Commun. Nonlinear. Sci. Numer. Simul., 60(2018), 72-91.
  • [15] B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy sets syst., 230(2013), 119-141.
  • [16] V. Lakshikantham, R.N. Mohapatra, Theory of fuzzy differential equations and applications, London, CRC Press, 2003.
  • [17] L. Sajedi, N. Eghbali, H. Aydi, Impulsive coupled system of fractional differential equations with Caputo-Katugampola fuzzy fractional derivative, Hindawi. J. Math., 13(2021).
  • [18] X. Chen, H. Gu, X. Wang, Existence and uniqueness for fuzzy differential equation with Hilfer-Katugampola fractional derivative, Adv. Differ. Equ., 2020(2020), 241.
  • [19] N.V. Hoa, H. Vu, T.M. Duc, Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach, Fuzzy Sets Syst., 375(2019), 70-99.
  • [20] N.V. Hoa, Fuzzy fractional functional differential equations under Caputo gH-differentiability, Commun. Nonlinear. Sci. Numer. Simul., 22(1-3)(2015), 1134-1157.
  • [21] D.F. Luo, T. Abdeljawad, Z.G. Luo, Ulam-Hyers stability results for a novel nonlinear nabla caputo fractional variable order difference system, Turk. J. Math., 45(1)(2021), 456-70.
  • [22] D. Luo, K. Shah, Z. Luo, On the novel Ulam-Hyers stability for a class of nonlinear y-Hilfer fractional differential equation with time-varying delays, Mediterr. J. Math., 16(5)(2019), 112.
  • [23] S. Rashid, F. Jarad, K.M. Abualnaja, On fuzzy Volterra-Fredholm integrodifferential equation associated with Hilfergeneralized proportional fractional derivative, AIMS Math., 6(2021), 10920-10946.
  • [24] H. Vu, J.M. Rassias, N.V. Hoa, Ulam-Hyers-Rassias stability for fuzzy fractional integral equations, Iran. J. Fuzzy syst., 17(2020), 17-27.
  • [25] X. Wang, D. Luo, Q. Zhu, Ulam-Hyers stability of Caputo type fuzzy fractional differential equation with time-delays, Chaos. Solitons. Fractals., 156(2022), 111822.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ravichandran Vıvek 0000-0002-1451-0875

Kangarajan K. 0000-0001-5556-2658

Dvivek Vivek 0000-0003-0951-8060

Elsayed Elsayed 0000-0003-0894-8472

Proje Numarası -
Erken Görünüm Tarihi 12 Eylül 2023
Yayımlanma Tarihi 17 Eylül 2023
Gönderilme Tarihi 28 Şubat 2023
Kabul Tarihi 25 Temmuz 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Vıvek, R., K., K., Vivek, D., Elsayed, E. (2023). Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses. Communications in Advanced Mathematical Sciences, 6(3), 115-127. https://doi.org/10.33434/cams.1257750
AMA Vıvek R, K. K, Vivek D, Elsayed E. Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses. Communications in Advanced Mathematical Sciences. Eylül 2023;6(3):115-127. doi:10.33434/cams.1257750
Chicago Vıvek, Ravichandran, Kangarajan K., Dvivek Vivek, ve Elsayed Elsayed. “Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations With Impulses”. Communications in Advanced Mathematical Sciences 6, sy. 3 (Eylül 2023): 115-27. https://doi.org/10.33434/cams.1257750.
EndNote Vıvek R, K. K, Vivek D, Elsayed E (01 Eylül 2023) Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses. Communications in Advanced Mathematical Sciences 6 3 115–127.
IEEE R. Vıvek, K. K., D. Vivek, ve E. Elsayed, “Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses”, Communications in Advanced Mathematical Sciences, c. 6, sy. 3, ss. 115–127, 2023, doi: 10.33434/cams.1257750.
ISNAD Vıvek, Ravichandran vd. “Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations With Impulses”. Communications in Advanced Mathematical Sciences 6/3 (Eylül 2023), 115-127. https://doi.org/10.33434/cams.1257750.
JAMA Vıvek R, K. K, Vivek D, Elsayed E. Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses. Communications in Advanced Mathematical Sciences. 2023;6:115–127.
MLA Vıvek, Ravichandran vd. “Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations With Impulses”. Communications in Advanced Mathematical Sciences, c. 6, sy. 3, 2023, ss. 115-27, doi:10.33434/cams.1257750.
Vancouver Vıvek R, K. K, Vivek D, Elsayed E. Dynamics and Stability of $\Xi$-Hilfer Fractional Fuzzy Differential Equations with Impulses. Communications in Advanced Mathematical Sciences. 2023;6(3):115-27.

Cited By

Some results on the study of -Hilfer type fuzzy fractional differential equations with time delay
Proceedings of International Mathematical Sciences
https://doi.org/10.47086/pims.1168552

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