Intuitionistic Fuzzy Riemann-Liouville and Hadamard Fractional ⊕⊗Integrals
Abstract
In this study, we introduce intuitionistic fuzzy Riemann-Liouville and Hadamard fractional ⊕⊗integrals of intuitionistic fuzzy valued functions and obtain some of their basic properties. We also give some examples to illustrate the obtained results.
References
Grossman, M., & Katz, R. (1972). Non-Newtonian calculus. Lee Press.
Stanley, D. (1999). A multiplicative calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 9(4), 310–326. https://doi.org/10.1080/10511979908965937
Abdeljawad, T., & Grossman, M. (2016). On geometric fractional calculus. Journal of Semigroup Theory and Applications, 2016, Article ID 2. https://scik.org/index.php/jsta/article/view/2546
Zhou, Z., & Du, T. S. (2024). Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals. Chaos, Solitons & Fractals, 189, 115715. https://doi.org/10.1016/j.chaos.2024.115715
Baş, U., Akkurt, A., Has, A., & Yildirim, H. (2025). Multiplicative Riemann–Liouville fractional integrals and derivatives. Chaos, Solitons & Fractals, 196, 116310. https://doi.org/10.1016/j.chaos.2025.116310
Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations (Vol. 204). Elsevier.
Budak, H., & Özçelik, K. (2020). On Hermite–Hadamard type inequalities for multiplicative fractional integrals. Miskolc Mathematical Notes, 21(1), 91–99. https://doi.org/10.18514/mmn.2020.3129
Fu, H., Peng, Y., & Du, T. S. (2021). Some inequalities for multiplicative tempered fractional integrals involving the λ-incomplete gamma functions. AIMS Mathematics, 6(7), 7456–7478. https://doi.org/10.3934/math.2021436
Peng, Y., & Du, T. S. (2024). On multiplicative (s, P)-convexity and related fractional inequalities within multiplicative calculus. Fractals, 32(3), 2450048. https://doi.org/10.1142/S0218348X24500488
Du, T. S., & Peng, Y. (2024). Hermite–Hadamard type inequalities for multiplicative Riemann–Liouville fractional integrals. Journal of Computational and Applied Mathematics, 440, 115582. https://doi.org/10.1016/j.cam.2023.115582
Du, T. S., & Long, Y. (2025). The multi-parameterized integral inequalities for multiplicative Riemann–Liouville fractional integrals. Journal of Mathematical Analysis and Applications, 541(1), 128692. https://doi.org/10.1016/j.jmaa.2024.128692
Yavuz, E. (2023). A calculus for intuitionistic fuzzy values. Turkish Journal of Mathematics, 47(2), 746–768. https://doi.org/10.55730/1300-0098.3392
Bashirov, A. E., Kurpınar, E. M., & Özyapıcı, A. (2008). Multiplicative calculus and its applications. Journal of Mathematical Analysis and Applications, 337(1), 36–48. https://doi.org/10.1016/j.jmaa.2007.03.081
Erdogan, M., & Duyar, C. (2018). Non-Newtonian improper integrals. Journal of Science and Arts, 1(42), 49–74.
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Deschrijver, G., & Kerre, E. E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133, 227–235. https://doi.org/10.1016/S0165-0114(02)00127-6
Deschrijver, G., Cornelis, C., & Kerre, E. E. (2004). On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems, 12(1), 45–61. https://doi.org/10.1109/TFUZZ.2003.822678
Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35, 417–433. https://doi.org/10.1080/03081070600574353
Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operations. IEEE Transactions on Fuzzy Systems, 15, 1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678
Atanassov, K. (2012). On intuitionistic fuzzy sets theory. Springer-Verlag. https://doi.org/10.1007/978-3-642-29127-2

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