
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,029 |
تعداد مشاهده مقاله | 67,082,929 |
تعداد دریافت فایل اصل مقاله | 7,656,387 |
Existence, uniqueness and continuous dependence of solution to random delay differential equation of fractional order | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 40، دوره 13، شماره 2، مهر 2022، صفحه 447-457 اصل مقاله (393.33 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25504.3036 | ||
نویسندگان | ||
Vu Ho* ؛ Dong Le Si | ||
Faculty of Mathematical Economics, Ho Chi Minh University of Banking, Vietnam | ||
تاریخ دریافت: 16 آذر 1400، تاریخ بازنگری: 25 فروردین 1401، تاریخ پذیرش: 12 اردیبهشت 1401 | ||
چکیده | ||
In this paper, we aim to prove the existence, uniqueness of the solution to the random delay differential equation of fractional order involving the successive approximation method. Moreover, using the Gronwall inequality, we study the continuous dependence of solution in the mean square sense of the problem. Finally, the fractional $\epsilon$-approximate solution in the mean square sense is also considered. | ||
کلیدواژهها | ||
Mean square calculus؛ Random differential equation؛ Fractional Stochastic Calculus؛ Random fractional differential equation | ||
مراجع | ||
[1] T. Abdeljawad, F. Madjidi, F. Jarad, and N. Sene, On dynamic systems in the frame of singular function dependent kernel fractional derivatives, Math. 7 (2019), no. 10. [2] A.Traore and N. Sene, Model of economic growth in the context of fractional derivative, Alexandria Engin. J. 59 (2020), no. 6, 4843–4850. [3] C. Burgos, J.-C. Cort´es, L. Villafuerte, and R.-J. Villanueva, Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density, J. Comput. Appl. Math. 378 (2020), 112925. [4] L.S. Dong, N.V. Hoa, and H. Vu, Existence and Ulam stability for random fractional integro-differential equation, Afr. Mat. 31 (2020), no. 7, 1283–1294. [5] A.M.A. El-Sayed, E.E. Eladdad, and H.F.A. Madkour, On the Cauchy problem of a delay stochastic differential equation of arbitrary (fractional) orders, Frac. Differ. Cal. 5 (2015), no. 2, 163–170. [6] H.Y. Frah and Z. Dahmani, Solvability for a sequential system of random fractional differential equations of Hermite type, J. Interdiscip. Math. (2022), 1–21. [7] H.Y. Frah, Z. Dahmani, L. Tabharit, and A. Abdelnebi, High order random fractional differential equations: Existence, uniqueness and data dependence, J. Interdiscip. Math. 24 (2021), no. 8, 2121–2138. [8] F.M. Hafiz, The fractional calculus for some stochastic processes, Stoch. Anal. Appl. 22 (2004), no. 2, 507–523. [9] F.M. Hafiz, Ahmed M.A. El-Sayed, and M.A. El-Tawil, On a stochastic fractional calculus, Frac. Cal. Appl. Anal. 4 (2001), no. 1, 81–90. [10] D. Henry, Geometric theory of semilinear parabolic equations, Springer, Berlin, Heidelberg, 1981. [11] R. Hilfer, Applications of fractional calculus in physics, World Scientific Publishing Company. [12] V. Ho, Random fractional functional differential equations, Int. J. Nonlinear Anal. Appl. 7 (2016), no. 2, 253–267. [13] C. Ionescu, A. Lopes, D. Copot, J.A.T. Machado, and J.H.T. Bates, The role of fractional calculus in modeling biological phenomena: A review, Commun. Nonlinear Sci. Numer. Simul. 51 (2017), 141–159.
[15] V. Lakshmikantham, S. Leela, and J. Vasundhara Devi, Theory of fractional dynamic systems, Cambridge Scientific Publishers, 2009. [16] V. Lupulescu and S.K. Ntouyas, Random fractional differential equations, Int. Electron. J. Pure Appl. Math. 4 (2012), no. 2, 119–136. [17] V. Lupulescu, D. O’Regan, and G. ur Rahman, Existence results for random fractional differential equations, Opuscula Math. 34 (2014), no. 4, 813–825. [18] N. Sene and A. Ndiaye, On class of fractional-order chaotic or hyperchaotic systems in the context of the Caputo fractional-order derivative, J. Math. 2020 (2020), 8815377. [19] N. Sene and G. Srivastava, Generalized Mittag-Leffler input stability of the fractional differential equations, Symmetry 11 (2019), no. 5. [20] X. Shen, Applications of fractional calculus in chemical engineering, Diss. Universit´e d’Ottawa/University of Ottawa, 2018. [21] I. Slimane and Z. Dahmani, A continuous and fractional derivative dependence of random differential equations with nonlocal conditions, J. Interdiscip. Math. 24 (2021), no. 6, 1457–1470. [22] T. T. Soong, Random differential equations in science and engineering, Academic Press, New York City, 1973. [23] H.-G. Sun, Y. Zhang, D. Baleanu, W. Chen, and Y.-Q. Chen, A new collection of real-world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci. Numer. Simul. 64 (2018), 213–231. [24] H. Vu and N. Van Hoa, On initial value problem of random fractional differential equation with impulses, Hacettepe J. Math. Statist. 49 (2020), no. 1, 282–293. [25] H. Vu, N.N. Phung, and N. Phuong, On fractional random differential equations with delay, Opuscula Math. 36 (2016), no. 4, 541–556. | ||
آمار تعداد مشاهده مقاله: 43,834 تعداد دریافت فایل اصل مقاله: 454 |