Open Access Open Access  Restricted Access Subscription or Fee Access

A Novel Numerical Method for Variable Fractional Order Cable Model


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/iremos.v13i5.19342

Abstract


The purpose of this paper is to apply a novel analytic algorithm based on Fractional Variational Iteration Method (FVIM) in order to examine the Multi-Dimensional Cable Equation with Variable Order Fractional with Non-Local Boundary Conditions Model (MDCEVOFNLBCM) with the Caputo variable time fractional derivative. In this method, initial and boundary conditions have been mixed together to get a new initial solution at every iteration. The convergence of method and the error estimation are given. The numerical analytical solution and some numerical examples show the accuracy and the efficiency of the proposed method, which is simple and accurate in comparison with exact. In addition, results are presented in Tables and Figure using both the MathCAD 12 and MATLAB software package.
Copyright © 2020 Praise Worthy Prize - All rights reserved.

Keywords


Multi-Dimensional; Initial Boundary Value Problems; Variational Iteration Method; Fractional Cable Equation; Caputo Derivatives

Full Text:

PDF


References


S. Jiang, J. Zhang, Z. Qian, Z. Zhang, Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations. Commun. Comput. Phys., 21, No 3, 650–678, 2017.
https://doi.org/10.4208/cicp.oa-2016-0136

Y. Bouras, D. Zorica, T.M. Atanackovic, Z. Vrcelj, A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete. Appl. Math. Model., 55, 551–568, 2018.
https://doi.org/10.1016/j.apm.2017.11.028

E. Shivanian, A. Jafarabadi, An improved meshless algorithm for a kind of fractional cable problem with error estimate. Chaos Solitons Fractals ,110, 138–151, 2018.
https://doi.org/10.1016/j.chaos.2018.03.013

Y. Chen, C. M. Chen, Novel numerical method of the fractional cable equation. Journal of Applied Mathematics and Computing 62, no. 1-2, 663-683, 2020.
https://doi.org/10.1007/s12190-019-01302-w

Naumova, N., Naumov, R., Method of Solving Some Optimization Problems for Dynamic Traffic Flow Distribution, (2018) International Review on Modelling and Simulations (IREMOS), 11 (4), pp. 245-251.
https://doi.org/10.15866/iremos.v11i4.13701

Hastuti, K., Azhari, A., Musdholifah, A., Supanggah, R., Rule-Based and Genetic Algorithm for Automatic Gamelan Music Composition, (2017) International Review on Modelling and Simulations (IREMOS), 10 (3), pp. 202-212.
https://doi.org/10.15866/iremos.v10i3.11479

SM. Aydogan, D. Baleanu, A. Mousalou, S. Rezapour, On approximate solutions for two higher-order Caputo-Fabrizio fractional integro-differential equations. Advances in Difference Equations, 221, 1-11, 2017.
https://doi.org/10.1186/s13662-017-1258-3

A. Atangana, J.F. Gomez-Aguilar, Fractional derivatives with no-index law property: application to chaos and statistics. Chaos Solitons Fractals, 114, 516–535, 2018.
https://doi.org/10.1016/j.chaos.2018.07.033

KM. Owolabi, A. Atangana, Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative. Chaos, Solitons Fractals.105:111-119, 2017.
https://doi.org/10.1016/j.chaos.2017.10.020

EFD. Goufo, S. Kumar, S. Mugisha, Similarities in a fifth-order evolution equation with and with no singular kernel. Chaos, Solitons Fractals., 130,109467, 2020.
https://doi.org/10.1016/j.chaos.2019.109467

E. Shivanian, A. Jafarabadi, The spectral meshless radial point interpolation method for solving an inverse source problem of the time-fractional diffusion equation. Appl. Numer. Math., 129, 1–25, 2018.
https://doi.org/10.1016/j.apnum.2018.02.008

E. Shivanian, A. Jafarabadi, Analysis of the spectral meshless radial point interpolation for solving fractional reaction-sub-diffusion equation. J. Comput. Appl. Math. 336, 98–113, 2018.
https://doi.org/10.1016/j.cam.2017.11.046

V.F. Morales-Delgado, On the solutions of fractional order of evolution equations. Eur. Phys. J. Plus, 132(1), 1–17, 2017.

N. H. Sweilam, & S. M. Al-Mekhlafi, . A novel numerical method for solving the 2-D time fractional cable equation. The European Physical Journal Plus, 134(7), 323, 2019.
https://doi.org/10.1140/epjp/i2019-12730-y

N.H. Sweilam1, S.M. AL-Mekhlafi, A novel numerical method for solving the 2-D time fractional cable equation, Eur. Phys. J. Plus. 134: 323, 2019.
https://doi.org/10.1140/epjp/i2019-12730-y

B. I. Henry, T. A. M. Langlands and S. L. Wearne Fractional cable models for spiny neuronal dendrites. Phys. Rev. Lett. 100 (12), 128103, 2008.
https://doi.org/10.1103/physrevlett.100.128103

E. G. Bazhlekova, and I. H. Dimovski, Exact solution for the fractional cable equation with nonlocal boundary conditions. Cent. Eur. J. Phys. 11 (10),1304–13131, 2013.
https://doi.org/10.2478/s11534-013-0213-5

N. H. Sweilam & T. A. Assiri, Non-Standard Crank-Nicholson Method for Solving the Variable Order Fractional Cable Equation. Appl. Math. Inf. Sci. 9, No. 2, 943-951,2015.

F. M. Coimbra, On the selection and Meaning of variable order operators for dynamic modeling, International Journal of Differential Equation, Vol. 2010, 1-16, 2010.

M. G. Sakar, H. Ergoren, Alternative variation iteration method for solving the time–fractional Fornberg-Whitham equation. Appl. Math. Model. 39(14),3972–3979, 2015.
https://doi.org/10.1016/j.apm.2014.11.048

Z. M. Odibat, A study on the convergence of variational iteration method, Math. Comput. Model., 51,1181–1192, 2010.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize