Research Article

A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL

Volume: 5 Number: 2 October 15, 2017
EN

A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL

Abstract

In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem. We give some examples.

Keywords

References

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  2. [2] R. Almeida, M. Guzowska and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, arXiv preprint arXiv:1612.00214.
  3. [3] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, in: Math. Studies., North-Holland, New York, 2006.
  4. [4] U. Katumgapola, A new fractional derivative with classical properties, preprint.
  5. [5] U.N. Katugampola, New Approach to a generalized fractional integral, Appl. Math. Comput. 218(3), (2011), 860-865.
  6. [6] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  7. [7] 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.
  8. [8] 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.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Merve Esra Yıldırım This is me
Türkiye

Publication Date

October 15, 2017

Submission Date

May 22, 2017

Acceptance Date

September 18, 2017

Published in Issue

Year 2017 Volume: 5 Number: 2

APA
Akkurt, A., Yıldırım, M. E., & Yıldırım, H. (2017). A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp Journal of Mathematics, 5(2), 248-259. https://izlik.org/JA94FN34KS
AMA
1.Akkurt A, Yıldırım ME, Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math. 2017;5(2):248-259. https://izlik.org/JA94FN34KS
Chicago
Akkurt, Abdullah, Merve Esra Yıldırım, and Hüseyin Yıldırım. 2017. “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”. Konuralp Journal of Mathematics 5 (2): 248-59. https://izlik.org/JA94FN34KS.
EndNote
Akkurt A, Yıldırım ME, Yıldırım H (October 1, 2017) A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp Journal of Mathematics 5 2 248–259.
IEEE
[1]A. Akkurt, M. E. Yıldırım, and H. Yıldırım, “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”, Konuralp J. Math., vol. 5, no. 2, pp. 248–259, Oct. 2017, [Online]. Available: https://izlik.org/JA94FN34KS
ISNAD
Akkurt, Abdullah - Yıldırım, Merve Esra - Yıldırım, Hüseyin. “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”. Konuralp Journal of Mathematics 5/2 (October 1, 2017): 248-259. https://izlik.org/JA94FN34KS.
JAMA
1.Akkurt A, Yıldırım ME, Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math. 2017;5:248–259.
MLA
Akkurt, Abdullah, et al. “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”. Konuralp Journal of Mathematics, vol. 5, no. 2, Oct. 2017, pp. 248-59, https://izlik.org/JA94FN34KS.
Vancouver
1.Abdullah Akkurt, Merve Esra Yıldırım, Hüseyin Yıldırım. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math. [Internet]. 2017 Oct. 1;5(2):248-59. Available from: https://izlik.org/JA94FN34KS
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