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Year 2021, Volume 9, Issue 1, 49 - 59, 28.04.2021

Abstract

References

  • [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

Year 2021, Volume 9, Issue 1, 49 - 59, 28.04.2021

Abstract

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.

References

  • [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.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Muhammet BOZKURT This is me
Kahramanmaras Sütcü Imam University
Türkiye


Abdullah AKKURT (Primary Author)
Kahramanmaraş Sütçü İmam Üniversitesi
0000-0001-5644-1276
Türkiye


Hüseyin YİLDİRİM
Kahramanmaras Sütcü Imam University
0000-0001-8855-9260
Türkiye

Publication Date April 28, 2021
Application Date July 2, 2020
Acceptance Date January 11, 2021
Published in Issue Year 2021, Volume 9, Issue 1

Cite

Bibtex @research article { konuralpjournalmath762802, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2021}, volume = {9}, pages = {49 - 59}, doi = {}, title = {Conformable Derivatives and Integrals for the Functions of Two Variables}, key = {cite}, author = {Bozkurt, Muhammet and Akkurt, Abdullah and Yildirim, Hüseyin} }
APA Bozkurt, M. , Akkurt, A. & Yildirim, H. (2021). Conformable Derivatives and Integrals for the Functions of Two Variables . Konuralp Journal of Mathematics (KJM) , 9 (1) , 49-59 . Retrieved from https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/31496/762802
MLA Bozkurt, M. , Akkurt, A. , Yildirim, H. "Conformable Derivatives and Integrals for the Functions of Two Variables" . Konuralp Journal of Mathematics (KJM) 9 (2021 ): 49-59 <https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/31496/762802>
Chicago Bozkurt, M. , Akkurt, A. , Yildirim, H. "Conformable Derivatives and Integrals for the Functions of Two Variables". Konuralp Journal of Mathematics (KJM) 9 (2021 ): 49-59
RIS TY - JOUR T1 - Conformable Derivatives and Integrals for the Functions of Two Variables AU - Muhammet Bozkurt , Abdullah Akkurt , Hüseyin Yildirim Y1 - 2021 PY - 2021 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 49 EP - 59 VL - 9 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2021 ER -
EndNote %0 Konuralp Journal of Mathematics (KJM) Conformable Derivatives and Integrals for the Functions of Two Variables %A Muhammet Bozkurt , Abdullah Akkurt , Hüseyin Yildirim %T Conformable Derivatives and Integrals for the Functions of Two Variables %D 2021 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 9 %N 1 %R %U
ISNAD Bozkurt, Muhammet , Akkurt, Abdullah , Yildirim, Hüseyin . "Conformable Derivatives and Integrals for the Functions of Two Variables". Konuralp Journal of Mathematics (KJM) 9 / 1 (April 2021): 49-59 .
AMA Bozkurt M. , Akkurt A. , Yildirim H. Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp J. Math.. 2021; 9(1): 49-59.
Vancouver Bozkurt M. , Akkurt A. , Yildirim H. Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp Journal of Mathematics (KJM). 2021; 9(1): 49-59.
IEEE M. Bozkurt , A. Akkurt and H. Yildirim , "Conformable Derivatives and Integrals for the Functions of Two Variables", Konuralp Journal of Mathematics (KJM), vol. 9, no. 1, pp. 49-59, Apr. 2021
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