GRONWALL TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS

Yıl 2016, Cilt: 4 Sayı: 2, 217 - 222, 01.10.2016

MEHMET ZEKI Sarıkaya

Öz

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.

Anahtar Kelimeler

Gronwall's inequality, confromable fractional integrals

Kaynakça

• [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 dierential 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.