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GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS

Year 2016, Volume: 4 Issue: 2, 217 - 222, 01.10.2016

MEHMET ZEKI Sarıkaya

Abstract

In this paper, some new generalized Gronwall-type inequalities are investigated for conformable differential equations. The established results are extensions of some existing Gronwall-type inequalities in the literature.

Keywords

Gronwall's inequality confromable fractional integrals

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57{66.
  • [2] D. R. Anderson and D. J. Ulness, Results for conformable di erential equations, preprint, 2016.
  • [3] A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Math. 2015; 13: 889{898.
  • [4] R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new de nition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [5] O.S. Iyiola and E.R.Nwaeze, Some new results on the new conformable fractional calculus with application using D'Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, 2016.
  • [6] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [7] M. Abu Hammad, R. Khalil, Abel's formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [8] U. Katugampola, A new fractional derivative with classical properties, ArXiv:1410.6535v2.
  • [9] A. Zheng, Y. Feng and W. Wang, The Hyers-Ulam stability of the conformable fractional differential equation, Mathematica Aeterna, Vol. 5, 2015, no. 3, 485-492.
  • [10] A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  • [11] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordonand Breach, Yverdon et alibi, 1993.

Year 2016, Volume: 4 Issue: 2, 217 - 222, 01.10.2016

MEHMET ZEKI Sarıkaya

Abstract

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57{66.
  • [2] D. R. Anderson and D. J. Ulness, Results for conformable di erential equations, preprint, 2016.
  • [3] A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Math. 2015; 13: 889{898.
  • [4] R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new de nition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [5] O.S. Iyiola and E.R.Nwaeze, Some new results on the new conformable fractional calculus with application using D'Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, 2016.
  • [6] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [7] M. Abu Hammad, R. Khalil, Abel's formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [8] U. Katugampola, A new fractional derivative with classical properties, ArXiv:1410.6535v2.
  • [9] A. Zheng, Y. Feng and W. Wang, The Hyers-Ulam stability of the conformable fractional differential equation, Mathematica Aeterna, Vol. 5, 2015, no. 3, 485-492.
  • [10] A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  • [11] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordonand Breach, Yverdon et alibi, 1993.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

MEHMET ZEKI Sarıkaya

Publication Date October 1, 2016
Submission Date June 4, 2014
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Sarıkaya, M. Z. (2016). GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 4(2), 217-222.
AMA Sarıkaya MZ. GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. Konuralp J. Math. October 2016;4(2):217-222.
Chicago Sarıkaya, MEHMET ZEKI. “GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 217-22.
EndNote Sarıkaya MZ (October 1, 2016) GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 2 217–222.
IEEE M. Z. Sarıkaya, “GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 4, no. 2, pp. 217–222, 2016.
ISNAD Sarıkaya, MEHMET ZEKI. “GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (October 2016), 217-222.
JAMA Sarıkaya MZ. GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:217–222.
MLA Sarıkaya, MEHMET ZEKI. “GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 217-22.
Vancouver Sarıkaya MZ. GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(2):217-22.
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