[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
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.
[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.
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. April 2021;9(1):49-59.
Chicago
Bozkurt, Muhammet, Abdullah Akkurt, and Hüseyin Yildirim. “Conformable Derivatives and Integrals for the Functions of Two Variables”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 49-59.
EndNote
Bozkurt M, Akkurt A, Yildirim H (April 1, 2021) Conformable Derivatives and Integrals for the Functions of Two Variables. Konuralp Journal of Mathematics 9 1 49–59.
IEEE
M. Bozkurt, A. Akkurt, and H. Yildirim, “Conformable Derivatives and Integrals for the Functions of Two Variables”, Konuralp J. Math., vol. 9, no. 1, pp. 49–59, 2021.
ISNAD
Bozkurt, Muhammet et al. “Conformable Derivatives and Integrals for the Functions of Two Variables”. Konuralp Journal of Mathematics 9/1 (April 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 et al. “Conformable Derivatives and Integrals for the Functions of Two Variables”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 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.