Research Article
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Conformable Fractional Calculus on Fuzzy Logic

Year 2021, Volume: 9 Issue: 1, 127 - 131, 28.04.2021

Abstract

In this article, we present a new general definition of fuzzy conformable
fractional derivative and fractional integral, that depends on an unknown
kernel. We will get some new applications with the help of this concept.

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] 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).
  • [3] M.E. Yıldırım, A. Akkurt and H. Yıldırım, On the Hadamard’s type inequalities for convex functions via conformable fractional integral, Journal of Inequalities and Special Functions, Volume 9 Issue 3(2018), Pages 1-10.
  • [4] 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 &Amp; Applications (IJOCTA), 9(1), 49–59, 2019. https://doi.org/10.11121/ijocta.01.2019.00559.
  • [5] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57–66.
  • [6] R. Almeida, M. Guzowska and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, Open Mathematics, vol. 14, no. 1, 2016, pp. 1122-1124. https://doi.org/10.1515/math-2016-0104
  • [7] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, in: Math. Studies., North-Holland, New York, 2006.
  • [8] B. Bede and L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems 230 (2013) 119–141.
  • [9] R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [10] S. Markov, “Calculus for interval functions of a real variable,” Computing, vol. 22, no. 4, pp. 325–337, 1979.
  • [11] O.A. Arqub and M. Al-Smadi, Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions. Soft Comput 24, 12501–12522 (2020). https://doi.org/10.1007/s00500-020-04687-0
  • [12] H. Y. Goo and J. S. Park, “On the continuity of the Zadeh extensions,” Journal of the Chungcheong Mathematical Society, vol. 20, no. 4, pp. 525–533, 2007.
  • [13] L. Stefanini, “A generalization of Hukuhara difference and division for interval and fuzzy arithmetic,” Fuzzy Sets and Systems, vol. 161, no. 11, pp. 1564–1584, 2010.
  • [14] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993
  • [15] 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.
  • [16] M. Z. Sarikaya, A. Akkurt, H. Budak, M.E. Turkay¨ and H. Yıldırım, On some special functions for conformable fractional integrals. Konuralp Journal of Mathematics, 8(2), 376-383.
  • [17] M.Z. Sarıkaya, Gronwall type inequalities for conformable fractional integrals. Konuralp Journal of Mathematics, 4(2), 217-222, 2016.
  • [18] F. Usta and M.Z. Sarıkaya, Some improvements of conformable fractional integral inequalities. International Journal of Analysis and Applications, 14(2), 162-166, 2017.
  • [19] F. Usta and M.Z. Sarıkaya, On generalization conformable fractional integral inequalities. Filomat, 32(16), 5519-5526, 2018.
  • [20] V. Lakshmikantham, R.N. Mohapatra, Theory of Fuzzy Differential Equations and Applications, Taylor & Francis, London (2003).
  • [21] L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338–353.
  • [22] M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, vol. 91, no. 2, pp. 552–558, 1983.
  • [23] G. A. Anastassiou and S. G. Gal, “On a fuzzy trigonometric approximation theorem of Weierstrass-type,” Journal of Fuzzy Mathematics, vol. 9, pp. 701–708, 2001.

Year 2021, Volume: 9 Issue: 1, 127 - 131, 28.04.2021

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] 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).
  • [3] M.E. Yıldırım, A. Akkurt and H. Yıldırım, On the Hadamard’s type inequalities for convex functions via conformable fractional integral, Journal of Inequalities and Special Functions, Volume 9 Issue 3(2018), Pages 1-10.
  • [4] 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 &Amp; Applications (IJOCTA), 9(1), 49–59, 2019. https://doi.org/10.11121/ijocta.01.2019.00559.
  • [5] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57–66.
  • [6] R. Almeida, M. Guzowska and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, Open Mathematics, vol. 14, no. 1, 2016, pp. 1122-1124. https://doi.org/10.1515/math-2016-0104
  • [7] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, in: Math. Studies., North-Holland, New York, 2006.
  • [8] B. Bede and L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems 230 (2013) 119–141.
  • [9] R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [10] S. Markov, “Calculus for interval functions of a real variable,” Computing, vol. 22, no. 4, pp. 325–337, 1979.
  • [11] O.A. Arqub and M. Al-Smadi, Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions. Soft Comput 24, 12501–12522 (2020). https://doi.org/10.1007/s00500-020-04687-0
  • [12] H. Y. Goo and J. S. Park, “On the continuity of the Zadeh extensions,” Journal of the Chungcheong Mathematical Society, vol. 20, no. 4, pp. 525–533, 2007.
  • [13] L. Stefanini, “A generalization of Hukuhara difference and division for interval and fuzzy arithmetic,” Fuzzy Sets and Systems, vol. 161, no. 11, pp. 1564–1584, 2010.
  • [14] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993
  • [15] 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.
  • [16] M. Z. Sarikaya, A. Akkurt, H. Budak, M.E. Turkay¨ and H. Yıldırım, On some special functions for conformable fractional integrals. Konuralp Journal of Mathematics, 8(2), 376-383.
  • [17] M.Z. Sarıkaya, Gronwall type inequalities for conformable fractional integrals. Konuralp Journal of Mathematics, 4(2), 217-222, 2016.
  • [18] F. Usta and M.Z. Sarıkaya, Some improvements of conformable fractional integral inequalities. International Journal of Analysis and Applications, 14(2), 162-166, 2017.
  • [19] F. Usta and M.Z. Sarıkaya, On generalization conformable fractional integral inequalities. Filomat, 32(16), 5519-5526, 2018.
  • [20] V. Lakshmikantham, R.N. Mohapatra, Theory of Fuzzy Differential Equations and Applications, Taylor & Francis, London (2003).
  • [21] L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338–353.
  • [22] M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, vol. 91, no. 2, pp. 552–558, 1983.
  • [23] G. A. Anastassiou and S. G. Gal, “On a fuzzy trigonometric approximation theorem of Weierstrass-type,” Journal of Fuzzy Mathematics, vol. 9, pp. 701–708, 2001.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Abdullah Akkurt 0000-0001-5644-1276

Submission Date April 9, 2021
Acceptance Date April 14, 2021
Publication Date April 28, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Akkurt, A. (2021). Conformable Fractional Calculus on Fuzzy Logic. Konuralp Journal of Mathematics, 9(1), 127-131. https://izlik.org/JA84SC93UH
AMA 1.Akkurt A. Conformable Fractional Calculus on Fuzzy Logic. Konuralp J. Math. 2021;9(1):127-131. https://izlik.org/JA84SC93UH
Chicago Akkurt, Abdullah. 2021. “Conformable Fractional Calculus on Fuzzy Logic”. Konuralp Journal of Mathematics 9 (1): 127-31. https://izlik.org/JA84SC93UH.
EndNote Akkurt A (April 1, 2021) Conformable Fractional Calculus on Fuzzy Logic. Konuralp Journal of Mathematics 9 1 127–131.
IEEE [1]A. Akkurt, “Conformable Fractional Calculus on Fuzzy Logic”, Konuralp J. Math., vol. 9, no. 1, pp. 127–131, Apr. 2021, [Online]. Available: https://izlik.org/JA84SC93UH
ISNAD Akkurt, Abdullah. “Conformable Fractional Calculus on Fuzzy Logic”. Konuralp Journal of Mathematics 9/1 (April 1, 2021): 127-131. https://izlik.org/JA84SC93UH.
JAMA 1.Akkurt A. Conformable Fractional Calculus on Fuzzy Logic. Konuralp J. Math. 2021;9:127–131.
MLA Akkurt, Abdullah. “Conformable Fractional Calculus on Fuzzy Logic”. Konuralp Journal of Mathematics, vol. 9, no. 1, Apr. 2021, pp. 127-31, https://izlik.org/JA84SC93UH.
Vancouver 1.Akkurt A. Conformable Fractional Calculus on Fuzzy Logic. Konuralp J. Math. [Internet]. 2021 Apr. 1;9(1):127-31. Available from: https://izlik.org/JA84SC93UH
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