Research Article
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Year 2017, Volume 5, Issue 2, 248 - 259, 15.10.2017

Abstract

References

  • [1] A. Akkurt, M.E. Yıldırım and H. Yıldırım , On Some Integral Inequalities for Conformable Fractional Integrals, Asian Journal of Mathematics and Computer Research, 15(3): 205-212, 2017.
  • [2] R. Almeida, M. Guzowska and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, arXiv preprint arXiv:1612.00214.
  • [3] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, in: Math. Studies., North-Holland, New York, 2006.
  • [4] U. Katumgapola, A new fractional derivative with classical properties, preprint.
  • [5] U.N. Katugampola, New Approach to a generalized fractional integral, Appl. Math. Comput. 218(3), (2011), 860-865.
  • [6] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  • [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] 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.
  • [9] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13(3), 2014, 177-183.
  • [10] 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.
  • [11] Samko, S.G.; Kilbas, A.A.; Marichev, O.I.: Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
  • [12] J. Vanterler da C. Sousa, E. Capelas de Oliveira, A new truncated M-fractional derivative unifying some fractional derivatives with classical properties, arXiv:1704.08187.
  • [13] J. Vanterler da C. Sousa, E. Capelas de Oliveira , M -fractional derivative with classical properties, arXiv:1704.08186.
  • [14] M. Z. Sarikaya, H. Budak and F.Usta, On generalized the conformable fractional calculus, RGMIA Research Report Collection, 19 (2016), Article 121, 7 pp.

A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL

Year 2017, Volume 5, Issue 2, 248 - 259, 15.10.2017

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.

References

  • [1] A. Akkurt, M.E. Yıldırım and H. Yıldırım , On Some Integral Inequalities for Conformable Fractional Integrals, Asian Journal of Mathematics and Computer Research, 15(3): 205-212, 2017.
  • [2] R. Almeida, M. Guzowska and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, arXiv preprint arXiv:1612.00214.
  • [3] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, in: Math. Studies., North-Holland, New York, 2006.
  • [4] U. Katumgapola, A new fractional derivative with classical properties, preprint.
  • [5] U.N. Katugampola, New Approach to a generalized fractional integral, Appl. Math. Comput. 218(3), (2011), 860-865.
  • [6] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  • [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] 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.
  • [9] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13(3), 2014, 177-183.
  • [10] 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.
  • [11] Samko, S.G.; Kilbas, A.A.; Marichev, O.I.: Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
  • [12] J. Vanterler da C. Sousa, E. Capelas de Oliveira, A new truncated M-fractional derivative unifying some fractional derivatives with classical properties, arXiv:1704.08187.
  • [13] J. Vanterler da C. Sousa, E. Capelas de Oliveira , M -fractional derivative with classical properties, arXiv:1704.08186.
  • [14] M. Z. Sarikaya, H. Budak and F.Usta, On generalized the conformable fractional calculus, RGMIA Research Report Collection, 19 (2016), Article 121, 7 pp.

Details

Subjects Engineering
Journal Section Articles
Authors

Abdullah AKKURT
0000-0001-5644-1276
Türkiye


Merve Esra YILDIRIM
0000-0003-4429-2685
Türkiye


Hüseyin YILDIRIM
0000-0001-8855-9260
Türkiye

Publication Date October 15, 2017
Application Date May 22, 2017
Acceptance Date September 18, 2017
Published in Issue Year 2017, Volume 5, Issue 2

Cite

Bibtex @research article { konuralpjournalmath315229, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {248 - 259}, doi = {}, title = {A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL}, key = {cite}, author = {Akkurt, Abdullah and Yıldırım, Merve Esra and Yıldırım, Hüseyin} }
APA Akkurt, A. , Yıldırım, M. E. & Yıldırım, H. (2017). A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL . Konuralp Journal of Mathematics (KJM) , 5 (2) , 248-259 . Retrieved from https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/28490/315229
MLA Akkurt, A. , Yıldırım, M. E. , Yıldırım, H. "A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL" . Konuralp Journal of Mathematics (KJM) 5 (2017 ): 248-259 <https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/28490/315229>
Chicago Akkurt, A. , Yıldırım, M. E. , Yıldırım, H. "A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL". Konuralp Journal of Mathematics (KJM) 5 (2017 ): 248-259
RIS TY - JOUR T1 - A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL AU - Abdullah Akkurt , Merve Esra Yıldırım , Hüseyin Yıldırım Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 248 EP - 259 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER -
EndNote %0 Konuralp Journal of Mathematics (KJM) A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL %A Abdullah Akkurt , Merve Esra Yıldırım , Hüseyin Yıldırım %T A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL %D 2017 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 5 %N 2 %R %U
ISNAD Akkurt, Abdullah , Yıldırım, Merve Esra , Yıldırım, Hüseyin . "A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL". Konuralp Journal of Mathematics (KJM) 5 / 2 (October 2017): 248-259 .
AMA Akkurt A. , Yıldırım M. E. , Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math.. 2017; 5(2): 248-259.
Vancouver Akkurt A. , Yıldırım M. E. , Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp Journal of Mathematics (KJM). 2017; 5(2): 248-259.
IEEE A. Akkurt , M. E. Yıldırım and H. Yıldırım , "A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL", Konuralp Journal of Mathematics (KJM), vol. 5, no. 2, pp. 248-259, Oct. 2017
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