Study of fuzzy fractional dynamic equations on time scales for S-correlated fuzzy functions

[1] R. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with
uncertainty, Nonlinear Analysis: Theory, Methods and Applications, 72 (2010), 2859-2862. https://doi.org/10.
1016/j.na.2009.11.029

[2] T. Allahviranloo, A. Armand, Z. Gouyandeh, Fuzzy fractional differential equations under generalized fuzzy Caputo
derivative, Journal of Intelligent and Fuzzy Systems, 26 (2014), 1481-1490. https://doi.org/10.3233/IFS-130831

[3] T. Allahviranloo, S. Salahshour, S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty,
Soft Computing, 16 (2012), 297-302. https://doi.org/10.1007/s00500-011-0743-y

[4] S. Arshad, V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Analysis: Theory,
Methods and Applications, 74 (2011), 3685-3693. https://doi.org/10.1016/j.na.2011.02.048

[5] F. M. Atici, D. C. Biles, A. Lebedinsky, An application of time scales to economics, Mathematical and Computer
Modelling, 43 (2006), 718-726. https://doi.org/10.1016/j.mcm.2005.08.014

[6] L. C. Barros, R. C. Bassanezi, W. A. Lodwick, A first course in fuzzy logic, fuzzy dynamical systems and Biomathematics:
Theory and applications, Springer, 2024. https://doi.org/10.1007/978-3-031-50492-1

[7] B. Bede, Mathematics of fuzzy sets and fuzzy logic, Studies in Fuzziness and Soft Computing, Springer, London,
2013. https://doi.org/10.1007/978-3-642-35221-8

[8] N. Benkhettou, S. Hassani, D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, Journal of
King Saud University-Science, 28 (2016), 93-98. https://doi.org/10.1016/j.jksus.2015.05.003

[9] M. Bohner, A. Peterson, Dynamic equations on time scale: An introduction with applications, Birkh¨auser, Boston,
2001. https://doi.org/10.1007/978-1-4612-0201-1

[10] S. Das, I. Pan, Fractional order signal processing: Introductory concepts and applications, Springer Science and
Business Media, 2011. https://doi.org/10.1007/978-3-642-23117-9

[11] E. Esmi, L. C. Barros, F. Santo Pedro, B. Laiate, Banach spaces generated by strongly linearly independent fuzzy
numbers, Fuzzy Sets and Systems, 417 (2021), 110-129. https://doi.org/10.1016/j.fss.2020.09.010

[12] S. Georgiev, Fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales, Springer,
2021.

[13] S. Hilger, Ein Maßkettenkalk¨ul mit anwendung auf zentrumsmannigfaltigkeiten, Ph. D. dissertation, University of
W¨urzburg, 1988.

[14] G. Liu, X. Xiang, Y. Peng, Nonlinear integro-differential equations and optimal control problems on time scales,
Computers and Mathematics with Applications, 61 (2011), 155-169. https://doi.org/10.1016/j.camwa.2010.
10.013

[15] F. C. Meral, T. J. Royston, R. Magin, Fractional calculus in viscoelasticity: An experimental study, Communications
in Nonlinear Science and Numerical Simulation, 15 (2010), 939-945. https://doi.org/10.1016/j.cnsns.
2009.05.004

[16] P. Prakash, J. J. Nieto, S. Senthilvelavan, Fuzzy fractional initial value problem, Journal of Intelligent and Fuzzy
Systems, 28 (2015), 2691-2704. https://doi.org/10.3233/IFS-151547

[17] M. Shahidi, T. Allahviranloo, M. Arana-Jim´enez, Calculus and study of fuzzy dynamic equations for fuzzy vector
functions on time scales, Fuzzy Sets and Systems, (2025), 109307. https://doi.org/10.1016/j.fss.2025.109307

[18] M. Shahidi, E. Esmi, Some properties of a new concept of fractional derivative for fuzzy functions on time
scales, International Conference on Intelligent and Fuzzy Systems, Springer, 2023. https://doi.org/10.1007/
978-3-031-39774-5_6

[19] M. Shahidi, E. Esmi, L. C. Barros, A study of fuzzy Volterra integral and dynamic equations for S-correlated fuzzy
process on time scales, Fuzzy Sets and Systems, 471 (2023), 108695. https://doi.org/10.1016/j.fss.2023.
108695

[20] M. Shahidi, A. Khastan, New fractional derivative for fuzzy functions and its applications on time scale, Nonlinear
Dynamics and Complexity: Mathematical Modelling of Real-World Problems, (2022), 337-354. https://doi.org/
10.1007/978-3-031-06632-0_16

[21] O. Solaymani Fard, T. A. Bidgoli, Calculus of fuzzy functions on time scales (I), Soft Computing, 19 (2015),
293-305. https://doi.org/10.1007/s00500-014-1252-6

[22] O. Solaymani Fard, T. A. Bidgoli, A. Rivaz, On existence and uniqueness of solutions to the fuzzy dynamic
equations on time scales, Mathematical and Computational Applications, 22 (2017), 16. https://doi.org/10.
3390/mca22010016

[23] H. Vu, N. V. Hoa, Uncertain fractional differential equations on a time scale under granular differentiability concept,
Computational and Applied Mathematics, 38 (2019), 110. https://doi.org/10.1007/s40314-019-0873-x

[24] Z. Zhan, W. Wei, Necessary conditions for a class of optimal control problems on time scales, Abstract and Applied
Analysis, 14 (2009). https://doi.org/10.1155/2009/974394