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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 Articles
Authors

Abdullah Akkurt 0000-0001-5644-1276

Publication Date April 28, 2021
Submission Date April 9, 2021
Acceptance Date April 14, 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.
AMA Akkurt A. Conformable Fractional Calculus on Fuzzy Logic. Konuralp J. Math. April 2021;9(1):127-131.
Chicago Akkurt, Abdullah. “Conformable Fractional Calculus on Fuzzy Logic”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 127-31.
EndNote Akkurt A (April 1, 2021) Conformable Fractional Calculus on Fuzzy Logic. Konuralp Journal of Mathematics 9 1 127–131.
IEEE A. Akkurt, “Conformable Fractional Calculus on Fuzzy Logic”, Konuralp J. Math., vol. 9, no. 1, pp. 127–131, 2021.
ISNAD Akkurt, Abdullah. “Conformable Fractional Calculus on Fuzzy Logic”. Konuralp Journal of Mathematics 9/1 (April 2021), 127-131.
JAMA 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, 2021, pp. 127-31.
Vancouver Akkurt A. Conformable Fractional Calculus on Fuzzy Logic. Konuralp J. Math. 2021;9(1):127-31.
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