Solutions to the fuzzy Pielou logistic differential equation

Document Type : Research Paper

Author

Department of Mathematics, Islamic Azad University, Savadkooh, Branch

Abstract

In this paper, the fuzzy Pielou logistic differential equation is studied from the perspective of the generalized Hukuhara differentiability concept. First, the uniqueness of positive or negative solutions is established. Then, the existence conditions of the solution, together with its structural representation, are obtained for two separate cases corresponding to the positivity or negativity of the fuzzy parameters of the problem. Detailed illustrative examples are also provided to clarify the results.

Keywords

Main Subjects

References

[1] A. Alamin, A. Akg¨ul, M. Rahaman, S. Prasad Mondal, S. Alam, Dynamical behaviour of discrete logistic equation
with Allee effect in an uncertain environment, Results in Control and Optimization, 12(4) (2023), 100254. https:
//doi.org/10.1016/j.rico.2023.100254
[2] T. Allahviranloo, M. Chehlabi, Solving fuzzy differential equations based on the length function properties, Soft
Computing, 19 (2015), 307-320. https://doi.org/10.1007/s00500-014-1254-4
[3] T. Allahviranloo, N. A. Kiani, M. Barkhordari, Toward the existence and uniqueness of solutions of second-order
fuzzy differential equations, Information Sciences, 179(8) (2009), 1207-1215. https://doi.org/10.1016/j.ins.
2008.11.004
[4] B. Bede, Mathematics of fuzzy sets and fuzzy logic, Springer, London, 2013. https://doi.org/10.1007/
978-3-642-35221-8
[5] B. Bede, S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to
fuzzy differential equations, Fuzzy Sets and Systems, 151(3) (2005), 581-599. https://doi.org/10.1016/j.fss.
2004.08.001
[6] B. Bede, J. Rudas, L. Bencsik, First order linear fuzzy differential equations under generalized differentiability,
Information Sciences, 177(7) (2007), 1648-1662. https://doi.org/10.1016/j.ins.2006.08.021
[7] B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 230 (2013),
119-141. https://doi.org/10.1016/j.fss.2012.10.003
[8] M. S. Cecconello, F. A. Dorini, G. Haeser, On fuzzy uncertainties on the logistic equation, Fuzzy Sets and Systems,
328 (2017), 107-121. https://doi.org/10.1016/j.fss.2017.07.011
[9] A. Celikyilmaz, I. Burhan T¨urksen, Modeling uncertainty with fuzzy logic, with recent theory and applications,
Springer-Verlag Berlin Heidelberg, 2009. https://doi.org/10.1007/978-3-540-89924-2
[10] Y. Chalco-Cano, H. Roman-Flores, On new solutions of fuzzy differential equations, Chaos, Solutions and Fractals,
38(1) (2008), 112-119. https://doi.org/10.1016/j.chaos.2006.10.043
[11] Y. Chalco-Cano, H. Roman-Flores, Comparation between some approaches to solve fuzzy differential equations,
Fuzzy Sets and Systems, 160(11) (2009), 1517-1527. https://doi.org/10.1016/j.fss.2008.10.002
[12] M. Chehlabi, Continuous solutions to a class of first-order fuzzy differential equations with discontinuous
coefficients, Computational and Applied Mathematics, 37 (2018), 5058-5081. https://doi.org/10.1007/
s40314-018-0612-8
[13] M. Chehlabi, T. Allahviranloo, Positive or negative solutions to first-order fully fuzzy linear differential equations
under generalized differentiability, Applied Soft Computing, 70 (2018), 359-370. https://doi.org/10.1016/j.
asoc.2018.05.040
[14] M. Chehlabi, T. Allahviranloo, Existence of generalized Hukuhara differentiable solutions to a class of first-order
fuzzy differential equations in dual form, Fuzzy Sets and Systems, 478 (2024), 108839. https://doi.org/10.1016/
j.fss.2023.108839
[15] A. De, S. Prakash Singh, Analysis of fuzzy applications in the agrisupply chain: A literature review, Journal of
Cleaner Production, 283 (2021), 124577. https://doi.org/10.1016/j.jclepro.2020.124577
[16] F. Delgado-Vences, F. Baltazar-Larios, A. Ornelas Vargas, E. Morales-Boj´oquez, V. H. Cruz-Escalona, C. Salom´on
Aguilar, Inference for a discretized stochastic logistic differential equation and its application to biological growth,
Journal of Applied Statistics, 50(6) (2022), 1231-1254. https://doi.org/10.1080/02664763.2021.2024154
[17] P. Diamond, P. Kloeden, Metric spaces of fuzzy sets: Theory and applications, World Scientific, Singapore, 1994.
https://doi.org/10.1142/2326
[18] H. Duan, X. Pang, A multivariate grey prediction model based on energy logistic equation and its application in
energy prediction in China, Energy, 229 (2021), 120716. https://doi.org/10.1016/j.energy.2021.120716
[19] B. Houchmandzadeh, Giant fluctuations in logistic growth of two species competing for limited resources, Physical
Review E, 98(4) (2018), 042118. https://doi.org/10.1103/PhysRevE.98.042118
[20] A. Khastan, Fuzzy logistic difference equation, Iranian Journal of Fuzzy Systems, 15(7) (2018), 55-66. https:
//doi.org/10.22111/ijfs.2018.4281
[21] A. Khastan, J. J. Nieto, R. Rodr´ıguez-L´opez, Fuzzy delay differential equations under generalized differentiability,
Information Sciences, 275 (2014), 145-167. https://doi.org/10.1016/j.ins.2014.02.027
[22] A. Khastan, R. Rodr´ıguez-L´opez, On the solutions to first order linear fuzzy differential equations, Fuzzy Sets and
Systems, 295 (2016), 114-135. https://doi.org/10.1016/j.fss.2015.06.005
[23] M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Rom´an-Flores, R. C. Bassanezi, Fuzzy differential equations
and the extension principle, Information Sciences, 177(17) (2007), 3627-3635. https://doi.org/10.1016/j.ins.
2007.02.039
[24] J. J. Nieto, R. Rodr´ıguez-L´opez, Analysis of a logistic differential model with uncertainty, International Journal
of Dynamical Systems and Differential Equations, 1(3) (2008), 164-176. https://doi.org/10.1504/IJDSDE.2008.
019678
[25] R. Rodr´ıguez-L´opez, On the existence of solutions to periodic boundary value problems for fuzzy linear differential
equations, Fuzzy Sets and Systems, 219 (2013), 1-26. https://doi.org/10.1016/j.fss.2012.11.007
[26] H. Rom´an-Flores, M. Rojas-Medar, Embedding of level-continuous fuzzy sets on Banach spaces, Information Sciences, 144(1-4) (2002), 227-247. https://doi.org/10.1016/S0020-0255(02)00182-2
[27] T. Rze˙zuchowski, J. Wa¸sowski, Differential equations with fuzzy parameters via differential inclusions, Journal of
Mathematical Analysis and Applications, 255(1) (2001), 177-194. https://doi.org/10.1006/jmaa.2000.7229
[28] A. Sadkowski, On the application of the logistic differential equation in electrochemical dynamics, Journal of Electroanalytical Chemistry, 486(1) (2000), 92-94. https://doi.org/10.1016/S0022-0728(00)00119-4
[29] H. M. Safuan, I. Towers, Z. Jovanoski, H. Sidhu, Coupled logistic carrying capacity model, The Proceedings of
ANZIAM Journal, 53 (2011), 172-184. https://doi.org/10.21914/anziamj.v53i0.4972
[30] S. Salahshour, A. Ahmadian, A. Mahata, S. P. Mondal, S. Alam, The behavior of logistic equation with alley effect
in fuzzy environment: Fuzzy differential equation approach, International Journal of Applied and Computational
Mathematics, 4(2) (2018), 62. https://doi.org/10.1007/s40819-018-0496-8
[31] B. Shiri, Z. Alijani, Y. Karaca, A power series method for the fuzzy fractional logistic differential equation, Fractals,
31(10) (2023), 113. https://doi.org/10.1142/S0218348X23400868
[32] V. E. Tarasov, V. V. Tarasova, Logistic equation with continuously distributed lag and application in economics,
Nonlinear Dynamics, 97 (2019), 1313-1328. https://doi.org/10.1007/s11071-019-05050-1
[33] J. H. M. Thornley, J. J. Shepherd, J. France, An open-ended logistic-based growth function: Analytical solutions
and the power-law logistic model, Ecological Modelling, 204(3-4) (2007), 531-534. https://doi.org/10.1016/j.
ecolmodel.2006.12.026
[34] R. M. Torresi, S. I. C´ordoba de Torresi, E. R. Gonzalez, On the use of the quadratic logistic differential equation for
the interpretation of electrointercalation processes, Journal of Electroanalytical Chemistry, 461(1-2) (1999), 161-166.
https://doi.org/10.1016/S0022-0728(98)00069-2
[35] C. Wu, Z. Gong, On Henstock integral of fuzzy-number-valued functions I, Fuzzy Sets and Systems, 120(3) (2001),
523-532. https://doi.org/10.1016/S0165-0114(99)00057-3
[36] Q. Zhang, F. Lin, X. Zhong, On discrete time Beverton-Holt population model with fuzzy environment, Mathematical
Biosciences and Engineering, 16(3) (2019), 1471-1488. https://doi.org/10.3934/mbe.2019071
Iranian Journal of Fuzzy Systems
Volume 23, Issue 1
January and February 2026
Pages 183-200

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