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فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

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Alikhani, Robab, Alamdari, Maryam. (1402). Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations. سامانه مدیریت نشریات علمی, 11(3), 440-463. doi: 10.22034/cmde.2023.50144.2084
Robab Alikhani; Maryam Alamdari. "Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations". سامانه مدیریت نشریات علمی, 11, 3, 1402, 440-463. doi: 10.22034/cmde.2023.50144.2084
Alikhani, Robab, Alamdari, Maryam. (1402). 'Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations', سامانه مدیریت نشریات علمی, 11(3), pp. 440-463. doi: 10.22034/cmde.2023.50144.2084
Alikhani, Robab, Alamdari, Maryam. Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations. سامانه مدیریت نشریات علمی, 1402; 11(3): 440-463. doi: 10.22034/cmde.2023.50144.2084

Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations

Computational Methods for Differential Equations
مقاله 2، دوره 11، شماره 3، شهریور 2023، صفحه 440-463    اصل مقاله (446.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.50144.2084
نویسندگان
Robab Alikhani؛ Maryam Alamdari*
Department of Mathematics, University of Tabriz, Tabriz, Iran.
چکیده
We aim at presenting results including analytical solutions to linear fully fuzzy Caputo-Fabrizio fractional differential equations. In such linear equations, the coefficients are fuzzy numbers and, as a useful approach, the cross product has been considered as a multiplication between the fuzzy data. This approach plays an essential role in simplifying of computation of analytical solutions of linear fully fuzzy problems. The obtained results have been applied for deriving explicit solutions of linear Caputo-Fabrizio differential equations with fuzzy coefficients and of the corresponding initial value problems. Some of the topics which are needed for the results of this study from the point of view of the cross product of fuzzy numbers have been explained in detail. We illustrate our technique and compare the effect of uncertainty of the coefficients and initial value on the related solutions.
کلیدواژه‌ها
Caputo-Fabrizio operator؛ Cross product؛ Initial value problem؛ Linear fuzzy differential equations
مراجع
  • [1] R. Abdollahi, A. khastan, J. J. Nieto, and R. Rodr´ıguez-L´opez, On the linear fuzzy model associated with Caputo- Fabrizio operator, Boundary Value problems, 1 (2018) 91.
  • [2] R. Abdollahi, M. B. Farshbaf Moghimi, A. Khastan, and M. R. Hooshmandasl, Linear fractional fuzzy differential equations with Caputo derivative, Computational Methods for Differential Equations, 7(2)(2019), 252-265.
  • [3] R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Analysis, 72 (2010), 2859-2862.
  • [4] R. Alikhani, F. Bahrami, and S. Parvizi, Differential calculus of fuzzy multi-variable functions and its application to fuzzy partial differential equations, Fuzzy Sets Syst., 375 (2019), 100-120.
  • [5] R. Alikhani and F. Bahrami, Fuzzy partial differential equations under the cross product of fuzzy numbers, Infor- mation Sciences, 494 (2019), 80-99.
  • [6] R. Alikhani and M. Mostafazadeh, First order linear fuzzy differential equations with fuzzy variable coefficients, Computational Methods for Differential Equations, 9(1) (2021), 1-21.
  • [7] R. Alikhani, Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets, Computational Methods for Differential Equations, 5(2017), 12-29.
  • [8] M. Alinezhad and T. Allahviranloo, On the solution of fuzzy fractional optimal control problems with the Caputo derivative, Information Sciences, 421 (2017), 218-236.
  • [9] T. Allahviranloo, Fuzzy fractional differential operators and equations, fuzzy fractional differential equations, Springer Nature, 397 (2020).
  • [10] S. Arshad and V. Lupulescu, Fractional differential equation with  the  fuzzy  initial  condition, Electronic Journal of Differential Equations, 2011(2011), 1-8.
  • [11] S. Arshad and V. Lupulescu, On the fractional differential equation with uncertainty, Nonlinear Analysis, 74 (2011), 3685-3693.
  • [12] F. Bahrami, R. Alikhani, and A. Khastan, Transport equation with fuzzy data, Iranian J. Fuzzy Syst., 15 (2018), 67-78.
  • [13] D. Baleanu, A. Mousalou, and S. Rezapour, On the existence of solutions for some infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential equations, Boundary Value Problems, 1 2017, 1-9.
  • [14] B. Bede, Mathematics of fuzzy sets and fuzzy logic, Springer, London, (2013).
  • [15] B. Bede and J. Foder, Product type operations between fuzzy Numbers and their applications in geology, Acta Polytechnica Hungarica, 3 (2006), 123-139.
  • [16] B. Bede and S. G. Gal, Solution of fuzzy differential equations based on generalized differentiablity, Commun.  Math. Anal., 9(2010), 22-41.
  • [17] B. Bede and S. G. Gal, Generalization of the differentiability of fuzzy-number-valued functions with applications  to fuzzy differential equations. Fuzzy Sets Syst., 151 (2005), 581-599.
  • [18] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1(2) (2015), 1-13.
  • [19] M. Chehlabi and T. Allahviranloo, Positive or negative solutions to first-order fully fuzzy linear differential equa- tions under generalized differentiability, Applied Soft Computing, 70 (2018), 359-370.
  • [20] P. Darabi, S. Moloudzadeh, and H. Khandani, A numerical method for solving first-order fully fuzzy differential equation under strongly generalized H-differentiability, Soft Computing, 20 (2016), 4085-4098.
  • [21] L. M. Dizaj Herik, M. Javidi, and M. Shafiee, A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability, Computational Methods for Differential Equations, 10(1) (2022), 12-27.
  • [22] M. A. Dokuyucu, E. Celik, H. Bulut, and H. M. Baskonus, Cancer treatment model with the Caputo-Fabrizio fractional derivative, The European Physical Journal Plus, 133(3) (2018), 1-6.
  • [23] E. Esmi,  D. E. S´anchez,  V. F. Wasques,  and L. C. de Barros,  Solutions  of  higher  order  linear  fuzzy  differential equations with interactive fuzzy values, Fuzzy Sets Syst., 419 (2021), 122-140.
  • [24] N. Gasilov, S. E. Amrahov, and A. G. Fatullayev, Solution of linear differential equations with fuzzy boundary values, Fuzzy Sets Syst., 257 (2014), 169-183.
  • [25] M. Ghaffari, T. Allahviranloo, S. Abbasbandy, and M. Azhini, On the fuzzy solutions of time-fractional problems, Iranian Journal of Fuzzy Systems, 18(3) (2021), 51-66.
  • [26] A. Jajarmi and B. Dumitru, A new iterative method for the numerical solution of high-order non-linear fractional boundary value problems, Frontiers in Physics, 8 (2020), 220.
  • [27] A. Khastan and R. Rodr´ıguez-L´opez, On the solution to first order fuzzy differential equations, Fuzzy Sets Syst., 295 (2016), 114-135.
  • [28] A.  Khastan  and  R.  Rodr´ıgeuz-L´opez,  On  linear  fuzzy  differential  equations  by  differential  inclusions’  approach, Fuzzy Sets Syst., 387 (2020), 49-67.
  • [29] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of fractional differential equations, Elsevier Science B. V., Amsterdam, (2006).
  • [30] H. V. Long, N. T. K. Son, and H. T. T. Tam, The solvability of fuzzy fractional  partial  differential  equations  under Caputo gH-differentiability, Fuzzy Sets Syst., 309(2017), 35-63.
  • [31] J. Losada and J. J. Nieto, Properties of new fractional derivative without singular kernel, prog. Fract. Differ. Appl., 1(2) (2015), 87-92.
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