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Towards Efficient Solutions of Space-Time Fractional Fuzzy Diffusion Equations: A Methodological Approach | ||
Iranian Journal of Fuzzy Systems | ||
دوره 21، شماره 4، مهر و آبان 2024، صفحه 179-195 اصل مقاله (2.14 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2024.48473.8544 | ||
نویسندگان | ||
Mohammad Mousavi Nasr1؛ Mohammad Sadegh Asgari* 2؛ Mohsen Ziamanesh1 | ||
1Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P.O. Box 13185/768, Tehran, Iran. | ||
2Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P.O. Box 13185/768, Tehran, Iran. | ||
چکیده | ||
This paper aims to introduce a groundbreaking methodology for deriving analytical solutions to the space-time fractional fuzzy diffusion equation. Our approach uniquely incorporates a Caputo generalized Hukuhara fractional derivative (of order $\beta \in (0,2]$) for the second-order spatial derivative, alongside a fuzzy Caputo-Katugampola generalized Hukuhara time-fractional derivative (of order $\alpha \in (0,1)$) for the first-order temporal derivative. The primary objective is to develop explicit and fundamental solutions for both the space-time fractional fuzzy diffusion equation and the time fractional fuzzy diffusion equation, encompassing various forms of fuzzy Caputo-Katugampola generalized Hukuhara time-fractional differentiability. We initiate our study by thoroughly analyzing the fuzzy Fourier and fuzzy $\wp-$Laplace transforms of the equation. To demonstrate the practical utility and effectiveness of our proposed method, we apply it to two specific models: a fuzzy groundwater flow model for computing pressure head, and a fuzzy model for determining the concentration of tumor cells. The results obtained highlight the method's efficiency and precision in addressing the complexities of both the space-time fractional fuzzy diffusion equation and the time fractional fuzzy diffusion equation. | ||
کلیدواژهها | ||
The fuzzy Caputo-Katugampola generalized Hukuhara time-fractional derivative؛ The fuzzy space-time fractional Diffusion equation؛ The fuzzy $\wp-$Laplace transform؛ the fuzzy Fourier transform؛ The Caputo generalized Hukuhara fractional derivative | ||
مراجع | ||
[1] T. Allahviranloo, Fuzzy fractional differential operators and equations: Fuzzy fractional differential equations, Germany, Springer International Publishing, (2020). https://doi.org/10.1007/978-3-030-51272-9 [2] T. Allahviranloo, Z. Gouyandeh, A. Armand, 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, Z. Gouyandeh, A. Armand, A. Hasanoglu, On fuzzy solutions for the heat equation based on generalized Hukuhara differentiability, Fuzzy Sets and Systems, 265 (2015), 1-23. https://doi.org/10.1016/j. fss.2014.11.009 [4] A. Alshbeel, A. Azmi, A. K. Alomari, Generalized Caputo-Katugampola for solving fuzzy fractional heat equation, Results in Nonlinear Analysis, 7(1) (2024), 44-63. https://doi.org/10.31838/rna/2024.07.01.006 [5] M. P. Anderson, W. W. Woessner, R. J. Hunt, Applied groundwater modeling: Simulation of flow and advective transport, Academic Press, (2015). https://doi.org/10.1016/C2009-0-21563-7 [6] A. Armand, T. Allahviranloo, Z. Gouyandeh, Some fundamental results on fuzzy calculus, Iranian Journal of Fuzzy Systems, 15(3) (2018), 27-46. https://doi.org/10.22111/IJFS.2018.3948 [7] A. Atangana, Mathematical analysis of groundwater flow models, CRC Press, (2022). https://doi.org/10.1201/ 9781003266266 [8] B. Bede, Mathematics of fuzzy sets and fuzzy logic, Springer, London, (2013). https://doi.org/10.1007/ 978-3-642-35221-8 [9] J. N. Del Pino, P. D’iaz, Pesticide distribution and movement. Biotherapy, 11 (1998), 69-76. https://doi.org/10. 1023/A:1007961524517 [10] H. Eghlimi, M. S. Asgari, A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative, Chaos, Solitons and Fractals, 175 (2023), 114007. https://doi.org/10.1016/j.chaos.2023. 114007 [11] M. Friedman, M. Ma, A. Kandel, Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and Systems, 106(1) (1999), 35-48. https://doi.org/10.1016/S0165-0114(98)00355-8 [12] M. Ghaffari, T. Allahviranloo, S. Abbasbandy, M. Azhini, On the fuzzy solutions of time-fractional problems, Iranian Journal of Fuzzy Systems, 18(3) (2021), 51-66. https://doi.org/10.22111/IJFS.2021.6081 [13] Z. Gouyandeh, T. Allahviranloo, S. Abbasbandy, A. Armand, A fuzzy solution of the heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets and Systems, 309 (2017), 81-97. https://doi. org/10.1016/j.fss.2016.04.010 [14] K. M. Hiscock, V. F. Bense, Hydrogeology: Principles and practice, Wiley-Blackwell, (2014). https://doi.org/ 10.1144/1470-9236/05-105 [15] N. V. Hoa, H. Vu, T. M. Duc, Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach, Fuzzy Sets and Systems, 375(15) (2019), 70-99. https://doi.org/10.1016/j.fss.2018.08.001 [16] J. Istok, Groundwater modeling by the finite element method (water resources monograph), American Geophysical Union, (1989). https://doi.org/10.1029/WM013 [17] F. Jarad, T. Abdeljawad, A modified Laplace transform for certain generalized fractional operators, Results in Nonlinear Analysis, 1(2) (2018), 88-98. [18] M. Keshavarz, T. Allahviranloo, Fuzzy fractional diffusion processes and drug release, Fuzzy Sets and Systems, 436 (2022), 82-101. https://doi.org/10.1016/j.fss.2021.04.001 [19] V. Lakshmikantham, T. Bhaskar, J. Devi, Theory of set differential equations in metric spaces, Cambridge Scientific Publishers, (2006). [20] J. D. Logan, Applied partial differential equations, Springer Cham, (2015). https://doi.org/10.1007/ 978-3-319-12493-3 [21] D. Mohapatra, S. Chakraverty, M. Alshammari, Time fractional heat equation of n + 1-dimension in Type- 1 and Type-2 fuzzy environment, International Journal of Fuzzy Systems, (2023). https://doi.org/10.1007/ s40815-023-01569-z [22] L. Sajedi, N. Eghbali, H. Aydi, Impulsive coupled system of fractional differential equations with Caputo- Katugampola fuzzy fractional derivative, Journal of Mathematics, (2021). https://doi.org/10.1155/2021/ 7275934 [23] S. Salahshour, T. Allahviranloo, Applications of fuzzy Laplace transforms, Soft Computing, 17 (2013), 145-158. https://doi.org/10.1007/s00500-012-0907-4 [24] W. Sawangtong, P. Sawangtong, An analytical solution for the Caputo type generalized fractional evolution equation, Alexandria Engineering Journal, 61 (2022), 5475-5483. https://doi.org/10.1016/j.aej.2021.10.055 [25] H. Viet Long, N. Thi Kim Son, H. Thi Thanh Tam, The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability, Fuzzy Sets and Systems, 309 (2017), 35-63. https://doi.org/10.1016/j.fss. 2016.06.018 [26] W. W. Woessner, E. P. Poeter, Hydrogeologic properties of earth materials and principles of groundwater flow, The Groundwater Project, (2020). https://books.gw-project.org/ hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow/. [27] H. C. Wu, The improper fuzzy Riemann integral and its numerical integration, Information Sciences, 111(14) (1998), 109-137. https://doi.org/10.1016/S0020-0255(98)00016-4 | ||
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