Year 2019, Volume 9, Issue 4, 792 - 799, 01.12.2019

M. Z. SARIKAYA H. BUDAK H. USTA

Abstract

ON GENERALIZED THE CONFORMABLE FRACTIONAL CALCULUS

Abstract

In this paper, we generalize the conformable fractional derivative and integral and obtain several results such as the product rule, quotient rule, chain rule.

Keywords

Confromable fractional derivative, confromable fractional integrals.

References

• Abdeljawad, T (2015), On conformable fractional calculus, Journal of Computational and Applied Mathematics 279, pp. 57–66.
• Anderson, D. R. (2016), Taylor’s formula and integral inequalities for conformable fractional deriva- tives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, New York.
• Hammad M. A. and Khalil R. (2014), Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), pp. 177-183.
• Hammad M. A. and Khalil R. (2014), Abel’s formula and wronskian for conformable fractional differ- ential equations, International Journal of Differential Equations and Applications 13(3), pp. 177-183.
• Iyiola O.S.and Nwaeze E.R.(2016), Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), pp.115-122.
• Khalil R., Al horani M., Yousef A. and Sababheh M.(2014), A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264, pp. 65-70.
• Katugampola U.N. (2011), New approach to a generalized fractional integral, Appl. Math. Comput., 218(3), pp. 860–865.
• Katugampola U.N. (2014), New approach to generalized fractional derivatives, B. Math. Anal. App., 6(4), pp. 1–15.
• Kilbas A. A., Srivastava H.M. and Trujillo J.J. (2016), Theory and Applications of Fractional Differ- ential Equations, Elsevier B.V., Amsterdam, Netherlands.
• Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993), Fractional Integrals and Derivatives: Theory and Applications, Yverdon: Gordon and Breach.