پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,532 |
| تعداد دریافت فایل اصل مقاله | 62,489,048 |
Approximate analytical solutions to delay fractional differential equations with Caputo derivatives of fractional variable orders and applications | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 15، شماره 9، آذر 2024، صفحه 1-11 اصل مقاله (561.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31083.4559 | ||
| نویسنده | ||
| Mathew O. Aibinu* | ||
| Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa | ||
| تاریخ دریافت: 07 تیر 1402، تاریخ بازنگری: 16 شهریور 1402، تاریخ پذیرش: 22 شهریور 1402 | ||
| چکیده | ||
| Fractional derivatives are suitable for describing several physical phenomena. The construction of efficient analytical and numerical methods for the solutions of ordinary and partial fractional differential equations is an active research area and it is of great interest to the researchers. The Caputo fractional derivative is of great use in the modelling and simulation of phenomena where consideration is given to the interactions within the past and problems with nonlocal properties. This study considers the use of a hybrid of the Sumudu Transform method for constructing the solution of nonlinear equations that describe the processes in the functional and structural materials. This study considers the models that are given by the integer-order derivatives, Caputo derivatives of fractional variable orders and Caputo derivatives of fractional variable orders that are associated with delays. The study applies a hybrid of Sumudu Transform to present solutions for each considered model and makes use of graphs to show the correlation among the models. The study is of great importance in the numerical and experimental characterization of the decay properties of functional and structural materials. | ||
| کلیدواژهها | ||
| Sumudu Transform؛ Caputo derivatives؛ Fractional؛ Decay؛ Model | ||
| مراجع | ||
|
[1] M.O. Aibinu and E. Momoniat, Approximate analytical solutions and applications of pantograph-type equations with Caputo derivative and variable orders, Appl. Math. Sci. Eng. 13 (2023), no. 1, 2232091. [2] M.O. Aibinu, S.C. Thakur, and S. Moyo, Analyzing population dynamics models via Sumudu transform, J. Math. Comput. Sci. 29 (2023), 283–294. [3] M.O. Aibinu, S.C. Thakur, and S. Moyo, Solving delay differential equations via Sumudu Transform, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 563–575. [4] F.B.M. Belgacem and A. Karaballi, Sumudu transform fundamental properties investigations and applications, J. Appl. Math. Stoch. Anal. 2006 (2006), Article ID: 91083. [5] F.B.M. Belgacem, A.A. Karaballi, and S.L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations, Math. Probl. Eng. 3 (2003), 103–118. [6] D.S. Bodkhe and S.K. Panchal, On Sumudu Transform of fractional derivatives and its applications to fractional differential equations, Asian J. Math. Comput Res. 11 (2016), no. 1, 69–77. [7] JR. Lamarsh and AJ. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001. [8] EE. Lewis and WF. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993. [9] O.E. Marcillo, M. Maceira, C. Chai, C. Gammans, R. Hunley, and C. Young, The local seismoacoustic wavefield of a research nuclear reactor and its response to reactor power level, Seismol. Res. Lett. 92 (2021), no. 1, 378–387. [10] A.T. Moltot, A.T. Deresse, and S.A. Edalatpanah, Approximate analytical solution to nonlinear delay differential equations by using Sumudu iterative method, Adv. Math. Phys. 2022 (2022), Article ID 2466367. [11] R.L. Murray, Nuclear Energy, Butterworth-Heinemann, 6th Ed., Chapter 6, 2008. [12] J.A. Nanware, N.G. Patil, and G.A. Birajdar, Applications of Sumudu transform to economic models, Pale J. Math. 11 (2022), no. 3, 636–649. [13] JR. Ockendon and AB. Tayler, The dynamics of a current collection system for an electric locomotive, Proc. R. Soc. Lond. A Math. Phys. Sci. 322 (1971), 447–468. [14] I. Petras, Fractional derivatives, fractional integrals, and fractional differential equations in Matlab, Assi A (ed) Engineering Education and Research Using MATLAB, 2011, pp. 239-264. [15] A.D. Polyanin and V.G. Sorokin, Nonlinear pantograph-type diffusion PDEs: Exact solutions and the principle of analogy, Mathematics 9 (2021), no. 5, 511. [16] P. Reuss, Neutron Physics, EDP Sciences, 2008. [17] W.M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001. [18] D. Tavares, R. Almeida, and D.F.M. Torres, Caputo derivatives of fractional variable order: Numerical approximations, Commun. Nonlinear Sci. Numer. Simul. 35 (2016), 69–87. [19] D.C. Tayal, Nuclear Physics, Himalaya Publishing House, 2009. [20] G.K.Watugala, Sumudu transform-a new integral transform to solve differential equations and control engineering problems, Math. Eng. Ind. 24 (1993), no. 1, 35–43. [21] WNA, World Nuclear Association (WNA) Image Library, https://www.world-nuclear.org/gallery/reactordiagrams/pressurized-water-reactor.aspx (Accessed 30 March, 2023). [22] G. Wu, Challenge in the variational iteration method-a new approach to identification of the Lagrange multipliers, J. King. Saud. Univ. Sci. 25 (2013), no. 2, 175–178. [23] G. Wu and D. Baleanu, Variational iteration method for fractional calculus-a universal approach by Laplace transform, Adv. Differ. Equ. 2013 (2013), no. 1, 1–9. [24] W. Zhang, D. Zhang, C. Wang, W. Tian, S. Qiu, and G.H. Su, Conceptual design and analysis of a megawatt power level heat pipe cooled space reactor power system, Ann. Nucl. Energy 144 (2020), 107576. | ||
|
آمار تعداد مشاهده مقاله: 1,410 تعداد دریافت فایل اصل مقاله: 1,124 |
||