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Yıl 2021, Cilt: 9 Sayı: 1, 49 - 59, 28.04.2021

Muhammet Bozkurt Abdullah Akkurt Hüseyin Yildirim

Öz

Kaynakça

  • [1] A. Akkurt, M. E. Yıldırım, and H. Yıldırım, A new Generalized fractional derivative and integral, Konuralp Journal of Mathematics, Volume 5 No. 2 pp. 248–259 (2017).
  • [2] M. Z. Sarıkaya, A. Akkurt, H. Budak, M. E. Yıldırım, and H. Yıldırım, Hermite-Hadamard’s inequalities for conformable fractional integrals. An Interna-tional Journal of Optimization and Control: Theories & Applications (IJOCTA), 9(1), 49-59 (2019). doi:http://dx.doi.org/10.11121/ijocta.01.2019.00559.
  • [3] R. Almeida, M. Guzowska, and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, Open Mathematics, 14(1), 1122-1124 (2016). doi: https://doi.org/10.1515/math-2016-0104
  • [4] D. R. Anderson, Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives. In: Pardalos P., Rassias T. (eds) Contributions in Mathematics and Engineering. Springer, 2016, Cham
  • [5] U. N. Katugampola, A new fractional derivative with classical properties, arXiv:1410.6535v1 [math.CA] 2014
  • [6] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Eqnarrays, in: Math. Studies., North-Holland, New York, 2006.
  • [7] S. G. Samko, A. A. Kilbas amd O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
  • [8] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  • [9] 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.
  • [10] F. Jarad, E. Ugurlu, T. Abdeljawad and D. Baleanu, On a new class of fractional operators, Advances in Difference Eqnarrays, 2017, 2017:247, https://doi.org/10.1186/s13662-017-1306-z
  • [11] D. P. Mourya, Fractional integrals of the functions of two variables. Proc. Indian Acad. Sci. 72, 173–184 (1970). https://doi.org/10.1007/BF03049707.
  • [12] M. Z. Sarikaya , On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, 25(2), 2014, pp:134-147.
  • [13] M.Z. Sarikaya, H. Budak and F. Usta, On generalized the conformable fractional calculus, TWMS J. App. Eng. Math. V.9, N.4, 2019, pp. 792-799.
  • [14] F. Jarad, E. Ugurlu˘ and T. Abdeljawad, On a new class of fractional operators. Adv Differ Equ 2017, 247 (2017). https://doi.org/10.1186/s13662-017-1306-z.

Conformable Derivatives and Integrals for the Functions of Two Variables

Yıl 2021, Cilt: 9 Sayı: 1, 49 - 59, 28.04.2021

Muhammet Bozkurt Abdullah Akkurt Hüseyin Yildirim

Öz

In this paper, we introduce conformable derivatives and integrals for the functions of two variables. This class of new fractional operators includes many definitions in the literature, such as Riemann-Liouville Fractional Derivatives and Integrals [6,7], Conformable Calculus [8,9], etc. In addition, some basic definitions and theorems have been obtained for these operators.

Anahtar Kelimeler

conformable integrals fractional derivatives fractional integrals

Kaynakça

  • [1] A. Akkurt, M. E. Yıldırım, and H. Yıldırım, A new Generalized fractional derivative and integral, Konuralp Journal of Mathematics, Volume 5 No. 2 pp. 248–259 (2017).
  • [2] M. Z. Sarıkaya, A. Akkurt, H. Budak, M. E. Yıldırım, and H. Yıldırım, Hermite-Hadamard’s inequalities for conformable fractional integrals. An Interna-tional Journal of Optimization and Control: Theories & Applications (IJOCTA), 9(1), 49-59 (2019). doi:http://dx.doi.org/10.11121/ijocta.01.2019.00559.
  • [3] R. Almeida, M. Guzowska, and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, Open Mathematics, 14(1), 1122-1124 (2016). doi: https://doi.org/10.1515/math-2016-0104
  • [4] D. R. Anderson, Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives. In: Pardalos P., Rassias T. (eds) Contributions in Mathematics and Engineering. Springer, 2016, Cham
  • [5] U. N. Katugampola, A new fractional derivative with classical properties, arXiv:1410.6535v1 [math.CA] 2014
  • [6] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Eqnarrays, in: Math. Studies., North-Holland, New York, 2006.
  • [7] S. G. Samko, A. A. Kilbas amd O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
  • [8] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57-66.
  • [9] 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.
  • [10] F. Jarad, E. Ugurlu, T. Abdeljawad and D. Baleanu, On a new class of fractional operators, Advances in Difference Eqnarrays, 2017, 2017:247, https://doi.org/10.1186/s13662-017-1306-z
  • [11] D. P. Mourya, Fractional integrals of the functions of two variables. Proc. Indian Acad. Sci. 72, 173–184 (1970). https://doi.org/10.1007/BF03049707.
  • [12] M. Z. Sarikaya , On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, 25(2), 2014, pp:134-147.
  • [13] M.Z. Sarikaya, H. Budak and F. Usta, On generalized the conformable fractional calculus, TWMS J. App. Eng. Math. V.9, N.4, 2019, pp. 792-799.
  • [14] F. Jarad, E. Ugurlu˘ and T. Abdeljawad, On a new class of fractional operators. Adv Differ Equ 2017, 247 (2017). https://doi.org/10.1186/s13662-017-1306-z.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Muhammet Bozkurt Bu kişi benim

Abdullah Akkurt 0000-0001-5644-1276

Hüseyin Yildirim 0000-0001-8855-9260

Yayımlanma Tarihi 28 Nisan 2021
Gönderilme Tarihi 2 Temmuz 2020
Kabul Tarihi 11 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Bozkurt, M., Akkurt, A., & Yildirim, H. (2021). Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp Journal of Mathematics, 9(1), 49-59.
AMA Bozkurt M, Akkurt A, Yildirim H. Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp J. Math. Nisan 2021;9(1):49-59.
Chicago Bozkurt, Muhammet, Abdullah Akkurt, ve Hüseyin Yildirim. “Conformable Derivatives and Integrals for the Functions of Two Variables”. Konuralp Journal of Mathematics 9, sy. 1 (Nisan 2021): 49-59.
EndNote Bozkurt M, Akkurt A, Yildirim H (01 Nisan 2021) Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp Journal of Mathematics 9 1 49–59.
IEEE M. Bozkurt, A. Akkurt, ve H. Yildirim, “Conformable Derivatives and Integrals for the Functions of Two Variables”, Konuralp J. Math., c. 9, sy. 1, ss. 49–59, 2021.
ISNAD Bozkurt, Muhammet vd. “Conformable Derivatives and Integrals for the Functions of Two Variables”. Konuralp Journal of Mathematics 9/1 (Nisan 2021), 49-59.
JAMA Bozkurt M, Akkurt A, Yildirim H. Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp J. Math. 2021;9:49–59.
MLA Bozkurt, Muhammet vd. “Conformable Derivatives and Integrals for the Functions of Two Variables”. Konuralp Journal of Mathematics, c. 9, sy. 1, 2021, ss. 49-59.
Vancouver Bozkurt M, Akkurt A, Yildirim H. Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp J. Math. 2021;9(1):49-5.
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