##### Title: On Comparison Theorems for Conformable Fractional Differential Equations

##### Pages: 207-214

##### Cite as:

Mehmet Zeki Sarikaya, Fuat Usta, On Comparison Theorems for Conformable Fractional Differential Equations, Int. J. Anal. Appl., 12 (2) (2016), 207-214.#### Abstract

In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

##### Full Text: PDF

#### References

- T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57–66.
- M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13(3), 2014, 177-183.
- M. Abu Hammad, R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, Inter- national Journal of Differential Equations and Applications 13(3), 2014, 177-183.
- D. R. Anderson, Taylor’s formula and integral inequalities for conformable fractional derivatives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, pp. 25-43, 2016.
- 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.
- R. Khalil, M. Al horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Compu- tational Apllied Mathematics, 264 (2014), 65-70.
- T. Khaniyev and M. Merdan, On the fractional Riccati differential equation, Int. J. of Pure and App. Math., 107(1) 2016, 145-160.
- U.N. Katugampola, A new fractional derivative with classical properties, arXiv:1410.6535v2
- [math.CA]
- U.N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 218(3) (2011), 860– 865.
- U.N. Katugampola, New approach to generalized fractional derivatives, B. Math. Anal. App., 6(4) (2014), 1–15.
- A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
- B. G. Pachpatte, Mathematical Inequalities, North-Holland Mathematical Library, Elsevier, 2005.
- M. Pospisil and L. P. Skripkova, Sturm’s theorems for conformable fractional differential equations, Math. Commun. 21 (2016), 273–281.
- S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gor- donand Breach, Yverdon et alibi, 1993.