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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,422
تعداد مقالات17,545
تعداد مشاهده مقاله56,827,361
تعداد دریافت فایل اصل مقاله18,838,918
Tarate, Shivaji, Bhadane, Ashok, Gaikwad, Shrikisan, Kshirsagar, Kishor. (1404). Semi-analytical solutions for time-fractional Cauchy reaction-diffusion equations via the new Elazki transform iterative method. سامانه مدیریت نشریات علمی, 13(4), 1201-1215. doi: 10.22034/cmde.2024.53470.2253
Shivaji Ashok Tarate; Ashok P Bhadane; Shrikisan B Gaikwad; Kishor Ashok Kshirsagar. "Semi-analytical solutions for time-fractional Cauchy reaction-diffusion equations via the new Elazki transform iterative method". سامانه مدیریت نشریات علمی, 13, 4, 1404, 1201-1215. doi: 10.22034/cmde.2024.53470.2253
Tarate, Shivaji, Bhadane, Ashok, Gaikwad, Shrikisan, Kshirsagar, Kishor. (1404). 'Semi-analytical solutions for time-fractional Cauchy reaction-diffusion equations via the new Elazki transform iterative method', سامانه مدیریت نشریات علمی, 13(4), pp. 1201-1215. doi: 10.22034/cmde.2024.53470.2253
Tarate, Shivaji, Bhadane, Ashok, Gaikwad, Shrikisan, Kshirsagar, Kishor. Semi-analytical solutions for time-fractional Cauchy reaction-diffusion equations via the new Elazki transform iterative method. سامانه مدیریت نشریات علمی, 1404; 13(4): 1201-1215. doi: 10.22034/cmde.2024.53470.2253

Semi-analytical solutions for time-fractional Cauchy reaction-diffusion equations via the new Elazki transform iterative method

Computational Methods for Differential Equations
مقاله 10، دوره 13، شماره 4، دی 2025، صفحه 1201-1215    اصل مقاله (4.07 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.53470.2253
نویسندگان
Shivaji Ashok Tarate* 1؛ Ashok P Bhadane2؛ Shrikisan B Gaikwad1؛ Kishor Ashok Kshirsagar1
1Department of Mathematics, New Arts, Commerce and Science College, Ahmednagar, Maharashtra, India.
2Department of Mathematics, Loknete Vyankatrao Hiray Arts, Science and Commerce College, Nashik, Maharashtra, India.
چکیده
In this article, the estimated analytic solutions for time-fractional Cauchy Reaction-Diffusion Equations (CRDE) are obtained using a New Elzaki Transform Iterative Method (NETIM). This method is the fusion of the Elzaki transform and the Iterative approach. The proposed technique is elegant and easy to adopt and comprehend. The semi-analytical results demonstrate, as this paper shows, a graphical interpretation of the solution using the mathematical software “Mathematica Wolform” and considering Caputo’s sense derivatives to analytical results, the suggested strategy is efficient and straightforward
کلیدواژه‌ها
Caputo fractional derivative؛ Elzaki transform؛ Cauchy reaction-diffusion equations
مراجع
  • [1] S. Abbasbandy and A. Shirzadi, An unconditionally stable finite difference scheme for equations of conservation law form, Italian Journal of Pure and Applied Mathematics, 37 (2017), 1–4.
  • [2] F. Ali, A. Zubair, M. Arif, I. Khan, and K. S. Nisar, A time fractional model of generalized Couette flow of couple stress nanofluid with heat and mass transfer: applications in engine oil, IEEE Access, 8 (2020), 146944–146966.
  • [3] M. Arif, F. Ali, I. Khan, and K. Nisar, A time fractional model with non–singular kernel the generalized Couette flow of couple stress nanofluid, IEEE Access, 8 (2020), 77378–77395.
  • [4] A. Atangana, Fractional operators with constant and variable order with application to geo–hydrology, Academic Press, (2017).
  • [5] S. Bhalekar and V. Daftardar-Gejji, Solving fractional–order logistic equation using a new iterative method, International Journal Of Differential Equations, 2012 (2012), 12.
  • [6] N. Britton, Reaction-diffusion equations and their applications to biology, (Academic Press/Harcourt Brace Jovanovich Publishers, 1998.
  • [7] V. Daftardar-Gejji and H. Jafari, An iterative method for solving nonlinear functional equations, Journal of mathematical analysis and applications, 316(2) (2006), 753–763.
  • [8] S. Das, Analytical solution of a fractional diffusion equation by variational iteration method, Computers And Mathematics With Applications, 57(3) (2009), 483–487.
  • [9] L. Debnath, Nonlinear partial differential equations for scientist and engineers, Birkhauser, 1997.
  • [10] M. Dehghan and S. Pourghanbar, Solution of the Black-Scholes equation for pricing of barrier option, Zeitschrift Fu¨r Naturforschung A, 66 (2011), 289–296.
  • [11] J. He, Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics And Computation, 135 (2003), 73–79.
  • [12] R. Jiwari, A higher order numerical scheme for singularly perturbed Burger–Huxley equation, J. Appl. Math. Inform., 29 (2011), 813–829.
  • [13] H. Khan, A. Khan, P. Kumam, D. Baleanu, and M. Arif, An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method, Advances In Difference Equations, 2020 (2020), 1–23.
  • [14] K. Kshirsagar, V. Nikam, S. Gaikwad, and S. Tarate, The double fuzzy Elzaki transform for solving fuzzy partial differential equations, Journal Of The Chungcheong Mathematical Society. 35 (2022), 177–196.
  • [15] S. Kumar, A new fractional modeling arising in engineering sciences and its analytical approximate solution, Alexandria Engineering Journal. 52 (2013), 813–819.
  • [16] S. Liao, On the homotopy analysis method for nonlinear problems, Appl Math Comput, 147 (2004), 499–513.
  • [17] J. Manafian and M. Lakestani, Lump-type solutions and interaction phenomenon to the bidirectional Sawada– Kotera equation, Pramana, 92 (2019), 1–13.
  • [18] R. C. Mittal and R. Jiwari, Numerical study of two-dimensional reaction–diffusion Brusselator system by differential quadrature method, International Journal for Computational Methods in Engineering Science and Mechanics, 12(1) (2011), 14–25.
  • [19] K. Nisar, A. Ciancio, K. Ali, M. Osman, C. Cattani, D. Baleanu, A. Zafar, M. Raheel, and M. Azeem, On beta–time fractional biological population model with abundant solitary wave structures, Alexandria Engineering Journal, 61 (2022), 1996–2008.
  • [20] R. Nuruddeen, Elzaki decomposition method and its applications in solving linear and nonlinear Schrodinger equations, Sohag Journal Of Mathematics, 4 (2017), 1–5.
  • [21] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier Science, (1998).
  • [22] M. Safari, D. Ganji, and M. Moslemi, Application of He’s variational iteration method and Adomian’s decomposition method to the fractional KdV–Burgers–Kuramoto equation, Comput Appl, 58 (2009), 2091–2097.
  • [23] S. Sharma and R. Bairwa, Iterative Laplace Transform Method for Solving Fractional Heat and Wave–Like Equations, Research Journal Of Mathematical And Statistical Sciences, 3 (2015), 4–9.
  • [24] N. Sheikh, M. Jamil, D. Ching, I. Khan, M. Usman, and K. Nisar, A generalized model for quantitative analysis of sediments loss: A Caputo time fractional model, Journal Of King Saud University–Science, 33 (2021), 101179.
  • [25] N. Smaoui and M. Zribi, Dynamics and control of the seven–mode truncation system of the 2–d Navier–Stokes equations, Communications In Nonlinear Science And Numerical Simulation, 32 (2016), 169–189.
  • [26] S. Tarate, A. Bhadane, S. Gaikwad, and K. Kshirsagar, Solution of time–fractional equations via Sumudu– Adomian decomposition method, Computational Methods For Differential Equations, 11 (2023), 345–356.
  • [27] S. Tarate, A. Bhadane, S. Gaikwad, and K. Kshirsagar, Sumudu–iteration transform method for fractional telegraph equations, J. Math. Comput. Sci., 12 (2022), Article ID 127.
  • [28] A. Wazwaz, A reliable modification of Adomian decomposition method, Appl Math Comput., 102 (1999), 77–86.
  • [29] B. Yildiz, O. Kilicoglu, and G. Yagubov, Optimal control problem for nonstationary Schr¨odinger equation, Numerical Methods For Partial Differential Equations: An International Journal, 25 (2009), 1195–1203.
  • [30] X. Zhong, J Vrijmoed, E. Moulas, and L. Tajˇcmanov´a, A coupled model for intragranular deformation and chemical diffusion, Earth And Planetary Science Letters, 474 (2017), 387–396.
  • [31] D. Ziane and M. H. Cherif. Resolution of nonlinear partial differential equations by Elzaki transform decomposition method, J. Appro. Theo. Appl. Math, 5 (2015), 17–30.
  • [32] D. Ziane, Elzaki transform and the decomposition method for nonlinear fractional partial differential equations, Int. J. Open Problems Compt. Math, 9(4) (2016).
آمار
تعداد مشاهده مقاله: 339
تعداد دریافت فایل اصل مقاله: 414


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب