Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 1 Sayı: 2, 106 - 112, 26.06.2018
https://doi.org/10.32323/ujma.419363

Öz

Kaynakça

  • [1] M. I. Abbas, Ulam stability of fractional impulsive differential equations with Riemann-Liouville integral boundary conditions Journal of Contemporary Mathematical Analysis, 2015, (50), 209-219.
  • [2] M. Benchohra, B. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations, Electronic Journal of Differential Equations, 10, (2009), 1-11.
  • [3] K. M. Furati, M. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving hilfer fractional derivative, Computer and Mathematics with Application, 64, (2012), 1616-1626.
  • [4] R. Hilfer, Applications of Fractional Calculus in Physics, World scientific, Singapore, 1999.
  • [5] R.W. Ibrahim , H.A. Jalab , Existence of Ulam stability for iterative fractional differential equations based on fractional entropy, Entropy 17 (5) (2015) 3172.
  • [6] R.W. Ibrahim, Ulam-Hyers stability for Cauchy fractional differential equation in the unit disk, Abstract Appl. Anal. (2012) 1.
  • [7] R.W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations, Int. J. Math. 23 (05) (2012) 1.
  • [8] R.W. Ibrahim, Ulam stability for fractional differential equation in complex domain, Abstract Appl. Anal. (2012) 1.
  • [9] R. Kamocki, C. Obczynski, On fractional Cauchy-type problems containing Hilfer’s derivative, Electronic Journal of Qualitative Theory of Differential Equations, 2016, 50, 1-12.
  • [10] R. Kamocki, A new representation formula for the Hilfer fractional derivative and its application, Journal of Computational and Applied Mathematics, 308, (2016), 39-45.
  • [11] U.N. Katugampola, Existence and uniqueness results for a class of generalized fractional differential equations, Bulletin of Mathematical Analysis and Applications, arXiv:1411.5229, v1 (2014). https://arxiv.org/abs/1411.5229.
  • [12] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World scientific, Singapore(1989).
  • [13] X. Liu, Y. Li, Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations, Abstract and Applied Analysis, (2014).
  • [14] Z. Luo, J. Shen, Global existence results for impulsive functional differential equation, Journal of Kathematical Analysis and Application, 323, (2006), 644-653.
  • [15] D. S. Oliveira, E. Capelas de oliveira, Hilfer-Katugampola fractional derivative, arxiv:1705.07733v1, 2017.
  • [16] A. Ouahab, Local and global existence and uniqueness results for impulsive differential equations with multiple delay, Journal of Mathematical Analysis and Application, 323, (2006), 456-472.
  • [17] J. Wang, L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electronic Journal of Qualitative Theory of Differential Equations, 63, (2011), 1-10.

Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator

Yıl 2018, Cilt: 1 Sayı: 2, 106 - 112, 26.06.2018
https://doi.org/10.32323/ujma.419363

Öz

In this note, we set up existence, uniqueness as well as the stability of a special class of fractional differential equation (FDE) with Hilfer-Katugampola fractional differential operator (HKFDO). The outcomes are given by employing the Schaefer's fixed point theorem and Banach contraction principle. Moreover, we modify the fractional Ulam stability (FUS) concept utilizing HKFDO.

Kaynakça

  • [1] M. I. Abbas, Ulam stability of fractional impulsive differential equations with Riemann-Liouville integral boundary conditions Journal of Contemporary Mathematical Analysis, 2015, (50), 209-219.
  • [2] M. Benchohra, B. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations, Electronic Journal of Differential Equations, 10, (2009), 1-11.
  • [3] K. M. Furati, M. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving hilfer fractional derivative, Computer and Mathematics with Application, 64, (2012), 1616-1626.
  • [4] R. Hilfer, Applications of Fractional Calculus in Physics, World scientific, Singapore, 1999.
  • [5] R.W. Ibrahim , H.A. Jalab , Existence of Ulam stability for iterative fractional differential equations based on fractional entropy, Entropy 17 (5) (2015) 3172.
  • [6] R.W. Ibrahim, Ulam-Hyers stability for Cauchy fractional differential equation in the unit disk, Abstract Appl. Anal. (2012) 1.
  • [7] R.W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations, Int. J. Math. 23 (05) (2012) 1.
  • [8] R.W. Ibrahim, Ulam stability for fractional differential equation in complex domain, Abstract Appl. Anal. (2012) 1.
  • [9] R. Kamocki, C. Obczynski, On fractional Cauchy-type problems containing Hilfer’s derivative, Electronic Journal of Qualitative Theory of Differential Equations, 2016, 50, 1-12.
  • [10] R. Kamocki, A new representation formula for the Hilfer fractional derivative and its application, Journal of Computational and Applied Mathematics, 308, (2016), 39-45.
  • [11] U.N. Katugampola, Existence and uniqueness results for a class of generalized fractional differential equations, Bulletin of Mathematical Analysis and Applications, arXiv:1411.5229, v1 (2014). https://arxiv.org/abs/1411.5229.
  • [12] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World scientific, Singapore(1989).
  • [13] X. Liu, Y. Li, Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations, Abstract and Applied Analysis, (2014).
  • [14] Z. Luo, J. Shen, Global existence results for impulsive functional differential equation, Journal of Kathematical Analysis and Application, 323, (2006), 644-653.
  • [15] D. S. Oliveira, E. Capelas de oliveira, Hilfer-Katugampola fractional derivative, arxiv:1705.07733v1, 2017.
  • [16] A. Ouahab, Local and global existence and uniqueness results for impulsive differential equations with multiple delay, Journal of Mathematical Analysis and Application, 323, (2006), 456-472.
  • [17] J. Wang, L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electronic Journal of Qualitative Theory of Differential Equations, 63, (2011), 1-10.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

S. Harikrishnan

Rabha Ibrahim

K. Kanagarajan

Yayımlanma Tarihi 26 Haziran 2018
Gönderilme Tarihi 28 Nisan 2018
Kabul Tarihi 10 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Harikrishnan, S., Ibrahim, R., & Kanagarajan, K. (2018). Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator. Universal Journal of Mathematics and Applications, 1(2), 106-112. https://doi.org/10.32323/ujma.419363
AMA Harikrishnan S, Ibrahim R, Kanagarajan K. Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator. Univ. J. Math. Appl. Haziran 2018;1(2):106-112. doi:10.32323/ujma.419363
Chicago Harikrishnan, S., Rabha Ibrahim, ve K. Kanagarajan. “Fractional Ulam-Stability of Fractional Impulsive Differential Equation Involving Hilfer-Katugampola Fractional Differential Operator”. Universal Journal of Mathematics and Applications 1, sy. 2 (Haziran 2018): 106-12. https://doi.org/10.32323/ujma.419363.
EndNote Harikrishnan S, Ibrahim R, Kanagarajan K (01 Haziran 2018) Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator. Universal Journal of Mathematics and Applications 1 2 106–112.
IEEE S. Harikrishnan, R. Ibrahim, ve K. Kanagarajan, “Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator”, Univ. J. Math. Appl., c. 1, sy. 2, ss. 106–112, 2018, doi: 10.32323/ujma.419363.
ISNAD Harikrishnan, S. vd. “Fractional Ulam-Stability of Fractional Impulsive Differential Equation Involving Hilfer-Katugampola Fractional Differential Operator”. Universal Journal of Mathematics and Applications 1/2 (Haziran 2018), 106-112. https://doi.org/10.32323/ujma.419363.
JAMA Harikrishnan S, Ibrahim R, Kanagarajan K. Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator. Univ. J. Math. Appl. 2018;1:106–112.
MLA Harikrishnan, S. vd. “Fractional Ulam-Stability of Fractional Impulsive Differential Equation Involving Hilfer-Katugampola Fractional Differential Operator”. Universal Journal of Mathematics and Applications, c. 1, sy. 2, 2018, ss. 106-12, doi:10.32323/ujma.419363.
Vancouver Harikrishnan S, Ibrahim R, Kanagarajan K. Fractional Ulam-stability of fractional impulsive differential equation involving Hilfer-Katugampola fractional differential operator. Univ. J. Math. Appl. 2018;1(2):106-12.

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