Page 96 - IJOCTA-15-1
P. 96
R. Hariharan, R. Udhayakumar / IJOCTA, Vol.15, No.1, pp.82-91 (2025)
[9] Abu Arqub, O. (2017). Adaptation of repro- [21] Zhu, Y., Rao, L. (2000). Differential inclusions
ducing kernel algorithm for solving fuzzy Fred- for fuzzy maps.Fuzzy Sets Systems, 112, 257-261.
holm–Volterra integrodifferential equations. Neu- https://doi.org/10.1016/S0165-0114(98)0
ral Computing and Applications, 28, 1591-1610. 0077-3
https://doi.org/10.1007/s00521-015-211 [22] Chen, X., Gu, H., & Wang, X. (2020). Exis-
0-x tence and uniqueness for fuzzy differential equa-
[10] Abu Arqub, O., Singh, J., & Alhodaly, M. (2023). tion with Hilfer–Katugampola fractional deriva-
Adaptation of kernel functions-based approach tive. Advances in Difference Equations, 2020, 1-
with Atangana–Baleanu–Caputo distributed or- 16. https://doi.org/10.1186/s13662-020-0
der derivative for solutions of fuzzy fractional 2696-9
Volterra and Fredholm integrodifferential equa- [23] Chen, M., Fu, Y., Xue, X., & Wu, C. (2008). Two-
tions. Mathematical Methods in the Applied Sci- point boundary value problems of undamped un-
ences, 46(7), 7807-7834. https://doi.org/10.1 certain dynamical systems. Fuzzy Sets and Sys-
002/mma.7228 tems, 159(16), 2077-2089.https://doi.org/10
[11] Katugampola, U. N. (2011). A new approach to .1016/j.fss.2008.03.006
generalized fractional derivatives. arXiv preprint [24] Katugampola, U. N. (2011). New approach to
arXiv:1106.0965. https://doi.org/10.48550/a a generalized fractional integral. Applied mathe-
rXiv.1106.0965 matics and computation, 218(3), 860-865. https:
[12] Hilfer, R. (Ed.). (2000). Applications of Fractional //doi.org/10.1016/j.amc.2011.03.062
Calculus in Physics. World scientific. [25] Pandey, R., Shukla, C., Shukla, A., Upadhyay,
[13] Gu, H., & Trujillo, J. J. (2015). Existence of mild A., & Singh, A. K. (2023). A new approach on
solution for evolution equation with Hilfer frac- approximate controllability of Sobolev-type Hilfer
tional derivative. Applied Mathematics and Com- fractional differential equations. An International
putation, 257, 344-354. https://doi.org/10.1 Journal of Optimization and Control: Theories &
016/j.amc.2014.10.083 Applications (IJOCTA), 13(1), 130-138. https:
[14] Oliveira, D. S., & De Oliveira, E. C. (2018). Hil- //doi.org/10.11121/ijocta.2023.1256
fer–Katugampola fractional derivatives. Compu- [26] Sahijwani, L., & Sukavanam, N. (2023). Approx-
tational and Applied Mathematics, 37(3), 3672- imate controllability for Riemann-Liouville frac-
3690. https://doi.org/10.1007/s40314-017 tional differential equations. International Jour-
-0536-8 nal of Optimization & Control: Theories & Ap-
[15] Bede, B., & Stefanini, L. (2013). Generalized dif- plications(IJOCTA), 13(1). https://doi.org/
ferentiability of fuzzy-valued functions. Fuzzy sets 10.11121/ijocta.2023.1178
and systems, 230, 119-141. https://doi.org/10 [27] Ghazouani, A. Z. I. Z., Amir, F. I. A., Elomari,
.1016/j.fss.2012.10.003 M. H., & Melliani, S. (2023). On the existence
[16] Chang, S. S., & Zadeh, L. A. (1972). On fuzzy and uniqueness of fuzzy mild solution of fractional
mapping and control. IEEE transactions on sys- evolution equations. Kragujevac Journal of Math-
tems, man, and cybernetics, (1), 30-34. https: ematics, 49(6), 949-966. https://doi.org/10.4
//doi.org/10.1109/TSMC.1972.5408553 6793/KgJMat2506.949G
[17] Agarwal, R. P., Lakshmikantham, V., & Nieto, J. [28] Sene, N., & Ndiaye, A. (2024). Existence and
J. (2010). On the concept of solution for fractional uniqueness study for partial neutral functional
differential equations with uncertainty. Nonlinear fractional differential equation under Caputo
Analysis: Theory, Methods & Applications, 72(6), derivative. An International Journal of Opti-
2859-2862. https://doi.org/10.1016/j.na.2 mization and Control: Theories & Applications
009.11.029 (IJOCTA), 14(3), 208-219. https://doi.org/10
[18] Abu Arqub, O., Singh, J., Maayah, B., & Al- .11121/ijocta.1464
hodaly, M. (2023). Reproducing kernel approach [29] Dineshkumar, C., Udhayakumar, R., Vijayaku-
for numerical solutions of fuzzy fractional ini- mar, V., Nisar, K. S., Shukla, A., Abdel-Aty, A.
tial value problems under the Mittag–Leffler ker- H., ... & Mahmoud, E. E. (2022). A note on ex-
nel differential operator. Mathematical Methods in istence and approximate controllability outcomes
the Applied Sciences, 46(7), 7965-7986. https: of Atangana-Baleanu neutral fractional stochastic
//doi.org/10.1002/mma.7305 hemivariational inequality. Results in Physics, 38,
[19] Arshad, S. (2013). On existence and uniqueness 105647. https://doi.org/10.1016/j.rinp.202
of solution of fuzzy fractional differential equa- 2.105647
tions. Iranian Journal of Fuzzy Systems, (2013)
Ramara Hariharan obtained his B.Sc. and M.Sc.
(10), 137-151. https://doi.org/10.22111/IJF
S.2013.1336 degrees in Mathematics from Bishop Heber College
[20] Allahviranloo, T., Armand, A., & Gouyandeh, Z. affiliated under Bharathidasan University, Tiruchi-
(2014). Fuzzy fractional differential equations un- rappalli, Tamil Nadu, India in 2020 and 2022, respec-
der generalized fuzzy Caputo derivative. Journal tively. Now, he is pursuing his Ph.D. degree under the
of Intelligent & Fuzzy Systems, 26(3), 1481-1490. guidance of Prof. R. Udhayakumar at the Department
https://doi.org/10.3233/IFS-130831 of Mathematics, School of Advanced Sciences, Vellore
90

