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A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL

Yıl 2017, Cilt: 5 Sayı: 2, 248 - 259, 15.10.2017

Öz

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.

Kaynakça

  • [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.
Yıl 2017, Cilt: 5 Sayı: 2, 248 - 259, 15.10.2017

Öz

Kaynakça

  • [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.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

Abdullah Akkurt 0000-0001-5644-1276

Merve Esra Yıldırım Bu kişi benim

Hüseyin Yıldırım

Yayımlanma Tarihi 15 Ekim 2017
Gönderilme Tarihi 22 Mayıs 2017
Kabul Tarihi 18 Eylül 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Akkurt, A., Yıldırım, M. E., & Yıldırım, H. (2017). A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp Journal of Mathematics, 5(2), 248-259.
AMA Akkurt A, Yıldırım ME, Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math. Ekim 2017;5(2):248-259.
Chicago Akkurt, Abdullah, Merve Esra Yıldırım, ve Hüseyin Yıldırım. “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”. Konuralp Journal of Mathematics 5, sy. 2 (Ekim 2017): 248-59.
EndNote Akkurt A, Yıldırım ME, Yıldırım H (01 Ekim 2017) A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp Journal of Mathematics 5 2 248–259.
IEEE A. Akkurt, M. E. Yıldırım, ve H. Yıldırım, “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”, Konuralp J. Math., c. 5, sy. 2, ss. 248–259, 2017.
ISNAD Akkurt, Abdullah vd. “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”. Konuralp Journal of Mathematics 5/2 (Ekim 2017), 248-259.
JAMA Akkurt A, Yıldırım ME, Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math. 2017;5:248–259.
MLA Akkurt, Abdullah vd. “A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL”. Konuralp Journal of Mathematics, c. 5, sy. 2, 2017, ss. 248-59.
Vancouver Akkurt A, Yıldırım ME, Yıldırım H. A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp J. Math. 2017;5(2):248-59.
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