Conformable Fractional Calculus on Fuzzy Logic

Yıl 2021, Cilt: 9 Sayı: 1, 127 - 131, 28.04.2021

Abdullah Akkurt

Öz

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.

Anahtar Kelimeler

Conformable fractional derivative, Fractional derivative and integrals, Fuzzy logic, Fuzzy fractional derivative

Kaynakça

• [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.