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A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values

Year 2015, Volume: 3 Issue: 2, 13 - 23, 19.01.2015

Behrouz Parsa Moghaddam Zeynab salamat Mostaghim

Abstract

In this paper, the method of fractional finite difference presents and used for solving a number of famous fractional orderversion of scientific models. The proposed method besides being simple is so exact which is sensible in the solved problems

Keywords

Finite difference method Caputo derivative; Fractional delay differential equations; Boundary conditions

References

  • Averina V., Kolmanovsky I., Gibson A., Song G., Bueler E. Analysis and control of delay-dependent behavior of engine air-to-fuel ratio. Proceedings of 2005 IEEE Conference on Control Applications (CCA 2005) 28, 1222–1227.
  • Bhalekar S. Dynamical analysis of fractional order Ucar prototype delayed system. vol. 6. Springer Verlag London Limited;(2012) 513–
  • Comte F. Operateurs fractionnaires en econometrie et en finance. Prepubl. MAP5. 2001.
  • Fall C.P., Marland E.S., Wagner J.M., Tyson J.J. Computational cell biology. New York: Springer-Verlag; 2002.
  • Feliu V., Rivas R., Castillo F. Fractional order controller robust to time delay for water distribution in an irrigation main canal pool. Comput Electron Agric 69(2), (2009) 185–97.
  • Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and Applications of Fractional Differential Equations, in: N. – Holl. Math. Stud. vol. 204, Elsevier Sci. B. V, Amst. 2006.
  • Landry M., Campbell S., Morris K., Aguilar C. Dynamics of an inverted pendulum with delayed Control, SIAM J.Appl. Dyn. Syst. 4(2005), 333 - 351.
  • Magin R. l. Fractional calculus of complex dynamics in biological tissues, Comput. Math. Appl. 59(5) (2010) 1586 - 1593.
  • Moghaddam B. P., Mostaghim Z. S. A Numerical method based on finite difference for solving fractional delay differential equations, J. Taibah Univ. Sci. 7 (2013) 120-127.
  • Moghaddam B. P., Mostaghim Z. S. A Novel Matrix Approach to Fractional Finite Difference for solving Models Based on Nonlinear Fractional Delay Differential Equations, Ain Shams Engineering Journal 5 (2014), 585–594.
  • Murray JD. Mathematical biology I: an introduction, inter appl. mathematics, 3rd ed., vol. 17. Berlin: Springer; 2002.
  • Park H., Hong K. S. Boundary control of container cranes, Proc. SPIE, Vol. 6042, 604210 (2005).

D*y(t) = f (t, y (t) , y (t *τ) , D*y(t), Dαy(t

Year 2015, Volume: 3 Issue: 2, 13 - 23, 19.01.2015

Behrouz Parsa Moghaddam Zeynab salamat Mostaghim

Abstract

References

  • Averina V., Kolmanovsky I., Gibson A., Song G., Bueler E. Analysis and control of delay-dependent behavior of engine air-to-fuel ratio. Proceedings of 2005 IEEE Conference on Control Applications (CCA 2005) 28, 1222–1227.
  • Bhalekar S. Dynamical analysis of fractional order Ucar prototype delayed system. vol. 6. Springer Verlag London Limited;(2012) 513–
  • Comte F. Operateurs fractionnaires en econometrie et en finance. Prepubl. MAP5. 2001.
  • Fall C.P., Marland E.S., Wagner J.M., Tyson J.J. Computational cell biology. New York: Springer-Verlag; 2002.
  • Feliu V., Rivas R., Castillo F. Fractional order controller robust to time delay for water distribution in an irrigation main canal pool. Comput Electron Agric 69(2), (2009) 185–97.
  • Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and Applications of Fractional Differential Equations, in: N. – Holl. Math. Stud. vol. 204, Elsevier Sci. B. V, Amst. 2006.
  • Landry M., Campbell S., Morris K., Aguilar C. Dynamics of an inverted pendulum with delayed Control, SIAM J.Appl. Dyn. Syst. 4(2005), 333 - 351.
  • Magin R. l. Fractional calculus of complex dynamics in biological tissues, Comput. Math. Appl. 59(5) (2010) 1586 - 1593.
  • Moghaddam B. P., Mostaghim Z. S. A Numerical method based on finite difference for solving fractional delay differential equations, J. Taibah Univ. Sci. 7 (2013) 120-127.
  • Moghaddam B. P., Mostaghim Z. S. A Novel Matrix Approach to Fractional Finite Difference for solving Models Based on Nonlinear Fractional Delay Differential Equations, Ain Shams Engineering Journal 5 (2014), 585–594.
  • Murray JD. Mathematical biology I: an introduction, inter appl. mathematics, 3rd ed., vol. 17. Berlin: Springer; 2002.
  • Park H., Hong K. S. Boundary control of container cranes, Proc. SPIE, Vol. 6042, 604210 (2005).
There are 12 citations in total.

Details

Journal Section Articles
Authors

Behrouz Parsa Moghaddam This is me

Zeynab salamat Mostaghim This is me

Publication Date January 19, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Moghaddam, B. P., & Mostaghim, Z. s. (2015). A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values. New Trends in Mathematical Sciences, 3(2), 13-23.
AMA Moghaddam BP, Mostaghim Zs. A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values. New Trends in Mathematical Sciences. January 2015;3(2):13-23.
Chicago Moghaddam, Behrouz Parsa, and Zeynab salamat Mostaghim. “A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations With Boundary Values”. New Trends in Mathematical Sciences 3, no. 2 (January 2015): 13-23.
EndNote Moghaddam BP, Mostaghim Zs (January 1, 2015) A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values. New Trends in Mathematical Sciences 3 2 13–23.
IEEE B. P. Moghaddam and Z. s. Mostaghim, “A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values”, New Trends in Mathematical Sciences, vol. 3, no. 2, pp. 13–23, 2015.
ISNAD Moghaddam, Behrouz Parsa - Mostaghim, Zeynab salamat. “A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations With Boundary Values”. New Trends in Mathematical Sciences 3/2 (January 2015), 13-23.
JAMA Moghaddam BP, Mostaghim Zs. A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values. New Trends in Mathematical Sciences. 2015;3:13–23.
MLA Moghaddam, Behrouz Parsa and Zeynab salamat Mostaghim. “A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations With Boundary Values”. New Trends in Mathematical Sciences, vol. 3, no. 2, 2015, pp. 13-23.
Vancouver Moghaddam BP, Mostaghim Zs. A Matrix Scheme Based on Fractional Finite Difference Method for Solving Fractional Delay Differential Equations with Boundary Values. New Trends in Mathematical Sciences. 2015;3(2):13-2.