We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Numerical Approach for Solving Fractional Pantograph Equation

by Ayse Anapali, Yalcin Ozturk, Mustafa Gulsu
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 113 - Number 9
Year of Publication: 2015
Authors: Ayse Anapali, Yalcin Ozturk, Mustafa Gulsu
10.5120/19857-1801

Ayse Anapali, Yalcin Ozturk, Mustafa Gulsu . Numerical Approach for Solving Fractional Pantograph Equation. International Journal of Computer Applications. 113, 9 ( March 2015), 45-52. DOI=10.5120/19857-1801

@article{ 10.5120/19857-1801,
author = { Ayse Anapali, Yalcin Ozturk, Mustafa Gulsu },
title = { Numerical Approach for Solving Fractional Pantograph Equation },
journal = { International Journal of Computer Applications },
issue_date = { March 2015 },
volume = { 113 },
number = { 9 },
month = { March },
year = { 2015 },
issn = { 0975-8887 },
pages = { 45-52 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume113/number9/19857-1801/ },
doi = { 10.5120/19857-1801 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:50:32.110197+05:30
%A Ayse Anapali
%A Yalcin Ozturk
%A Mustafa Gulsu
%T Numerical Approach for Solving Fractional Pantograph Equation
%J International Journal of Computer Applications
%@ 0975-8887
%V 113
%N 9
%P 45-52
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of linear algebraic equation using Maple 14 and we obtain the coefficients of Taylor expansion. In addition illustrative example is presented to demonstrate the effectiveness of the proposed method.

References
  1. R. Hilfer (Ed. ), Applications of Fractional Calculus in Physics, Academic Press, Orlando, 1999.
  2. I. Podlubny, Fractional Differential Equations, Academic Press, NewYork, 1999.
  3. A. M. Spasic, M. P. Lazarevic, Electroviscoelasticity of liquid/liquid interfaces: fractional-order model, J. Colloid Interface Sci. 282 (2005) 223–230.
  4. Muroya, Y. , E. Ishiwata and H. Brunner, 2003. On the attainable order of collocation methods for pantograph integro-differential equations. J. Comput. Appl. Math. , 152: 347- 366
  5. Shadia, M. , 1992. Numerical Solution of Delay Differential and Neutral Differential Equations Using Spline Methods. Ph. D Thesis, Assuit University
  6. Li, D. and M. Z. Liu, 2005. Runge-Kutta methods for the multi-pantograph delay equation. Appl. Math. Comput. , 163: 383-395.
  7. Evans, D. J. and K. R. Raslan, 2005. The Adomian decomposition method for solving delay differential equation. Int. J. Comput. Math. , 82 (1): 49-54
  8. E. Yusufoglu, An efficient algorithm for solving generalized pantograph equations with linear functional argument, App. Math. Comp. , 217 (2010) 3591–3595
  9. Sezer M, Yalcinbas S, Sahin N. Approximate solution of multi-pantograph equation with variable coeffi-cients. J Comput Appl Math, 2008, 214: 406–416
  10. Yu Z H. Variational iteration method for solving the multi-pantograph delay equation. Phys Lett A, 2008,372: 6475–6479
  11. Liu M Z, Li D. Properties of analytic solution and numerical solution of multi-pantograph equation. Appl Math Comput, 2004, 155: 853–871
  12. Z. Fan, M. Liu, W. Cao, Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations, J. Math. Anal. Appl. 325 (2007) 1142–1159.
  13. S. Momani,Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos, Solitons and Fractals 31 (2007) 1248–1255.
  14. S. S. Ray, R. K. Bera, Solution of an extraordinary dfferential equation by Adomian decomposition method, J. Appl. Math. 4 (2004) 331–338.
  15. A. M. A. El-Sayed, I. L. El-Kalla, E. A. A. Ziada, Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations, Appl. Numer. Math. 60 (2010) 788–797.
  16. O. Abdulaziz, I. Hashim, S. Momani, Application of homotopy-perturbation method to fractional IVPs, J. Comput. Appl. Math. 216 (2008) 574–584.
  17. S. Yanga, A. Xiao, H. Su, Convergence of the variational iteration method for solving multi-order fractional differential equations, Comput. Math. Appl. 60 (2010) 2871–2879.
  18. Z. Odibat, S. Momani, H. Xu, A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations, Appl. Math. Model. 34 (2010) 593–600.
  19. E. H. Doha, A. H. Bhrawy, S. S. Ezz-Eldien, A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order, Computers and Mathematics with Applications 62 (2011) 2364–2373.
  20. M. Gülsu, M. Sezer, A Taylor polynomial approach for solving differential difference equations, J. Comp. Appl. Math. 186 (2006) 349–364.
  21. M. Sezer, Taylor polynomial solution of Volterra Integral equations, Internat. J. Math. Ed. Sci. Technol. 25 (1994) 625–633.
  22. A. Karamete, M. Sezer, A Taylor collocation method for the solution of linear integrodifferential equations, Int. J. Comput. Math. 79 (2002) 987–1000.
  23. M. Gulsu, M. Sezer, Approximations to the solution of linear Fredholm integro-differential-difference equation of high order, J. Franklin Inst. 343 (2006) 720-737.
  24. M. Sezer, M. Gulsu, Polynomial solution of the most general linear Fredholm-Volterra integro differential-difference equations by means of Taylor ollocation method, Appl. Math. Comput. 185 (2007) 646-657.
  25. M. Gülsu, Y. Öztürk, M. Sezer, A new collocation method for solution of mixed linear integro differential difference equations, Appl. Math. Comp. 216 (2010) 2183-2198.
  26. Z. Odibat, N. T. Shawagfeh, Generalized Taylor's Formula. Appl. Math. Comput. 186 (2007) 286–293.
  27. Y. Keskin, O. Karao?lu, S. servi, G. Oturaç, The approximate solution of high order linear fractional ifferential equations with variable coefficients in terms of generalized Taylor polynomials, Math. Comp. Appl. 16 (2011) 617-629.
  28. Saeedi L. , Tari A. , Masuleh Momami H. S. 2013. Nuerical Solution of Some Nonlinear Volterra Integral Equations of First Kind, App. App. Math. 1932-9466.
Index Terms

Computer Science
Information Sciences

Keywords

Fractional pantograph equation pantograph equation fractional differential equation mathematical model collocation method approximate solution

Powered by PhDFocusTM