EDP Sciences logo
Web of Conferences logo
Search
Menu
All issues Volume 29 (2019) ITM Web Conf., 29 (2019) 01001 References
Open Access
Issue
ITM Web Conf.
Volume 29, 2019
1st International Conference on Computational Methods and Applications in Engineering (ICCMAE 2018)
Article Number 01001
Number of page(s) 8
Section Applied/Computational Mathematics
DOI https://doi.org/10.1051/itmconf/20192901001
Published online 15 October 2019
  1. Oldham K.B, Spanier J. The Fractional Calculus, Academic Press: New York. 1974. [Google Scholar]
  2. Miller K.S, Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley: New York. 1993. [Google Scholar]
  3. Bagley R.L, Torvik P.J. Fractional calculus in the transient analysis of viscoelastically damped structures, AIAA J. 1985; 23: 918–925. [CrossRef] [Google Scholar]
  4. Chow T.S. Fractional dynamics of interfaces between soft-nanoparticles and rough substrates, Phys. Lett. A. 2005; 342: 148–155. [CrossRef] [Google Scholar]
  5. Gaul L, Klein P, Kemple S. Damping description involving fractional operators, Mech. Syst. Signal. Pr. 1991; 5: 81–88. [CrossRef] [Google Scholar]
  6. Suarez L, Shokooh A. An eigenvector expansion method for the solution of motion containing fractional derivatives, J. Appl. Mech. 1997; 64: 629–735. [CrossRef] [Google Scholar]
  7. Podlubny I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Academic Press, New York. 1998. [Google Scholar]
  8. Momani S, Al-Khaled K. Numerical solutions for systems of fractional differential equations by the decomposition method, Appl. Math. Comput. 2005; 162: 1351–1365. [Google Scholar]
  9. Odibat Z, Momani S. Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul. 2006; 7: 27–34. [CrossRef] [Google Scholar]
  10. Meerschaert M, Tadjeran C. Finite difference approximations for two-sided space- fractional partial differential equations, Appl. Numer. Math. 2006; 56: 80–90. [CrossRef] [MathSciNet] [Google Scholar]
  11. Odibat Z, Shawagfeh N. Generalized Taylor's formula, Appl. Math. Comput. 2007; 186: 286–293. [Google Scholar]
  12. Arikoglu A, Ozkol I. Solution of fractional integro-differential equations by using fractional differential transform method, Chaos Solitons Fract 2009; 40: 521–529. [CrossRef] [Google Scholar]
  13. Hashim I, Abdulaziz O, Momani S. Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci. Numer. Simul. 2009; 14: 674–684. [CrossRef] [Google Scholar]
  14. Chen C.F, Hsiao C.H. A Walsh series direct method for solving variational problems, J. Frank. Inst. 1975; 300: 265–280. [CrossRef] [Google Scholar]
  15. Razzaghi M, Ordokhani Y. An application of rationalized Haar functions for variational problems, Appl. Math. Comput. 2001; 122: 353–364. [Google Scholar]
  16. Razzaghi M, Yousefi S. Legendre wavelets method for the solution of nonlinear problems in the calculus of variations, Math. Comput. Model. 2001; 34: 45–54. [CrossRef] [Google Scholar]
  17. Razzaghi M, Marzban H. Hybrid analysis direct method in the calculus of variations, Int. J. Comput. Math. 2000; 75: 259–269. [CrossRef] [Google Scholar]
  18. Razzaghi M, Marzban H. Direct method for variational problems via hybrid of blockpulse and Chebyshev functions, Math. Prob. Eng. 2000; 6: 85–97. [CrossRef] [Google Scholar]
  19. Marzban H, Razzaghi M. Analysis of time-delay systems via hybrid of block-pulse functions and Taylor series, J. Vibr. Contr. 2005; 11: 1455–1468. [CrossRef] [Google Scholar]
  20. Haddadi N, Ordokhani Y, Razzaghi M. Optimal Control of Delay Systems by Using a Hybrid Functions Approximation, J. Optimi. Theo. Appli. 2012; 153: 338–356. [CrossRef] [Google Scholar]
  21. Marzban, H. R., 2016, “Parameter identification of linear multi-delay systems via a hybrid of block-pulse functions and Taylors polynomials,” Int. J. Control., 1, pp. 1–15. [Google Scholar]
  22. Mashayekhi, S., and Razzaghi, M., 2015, “Numerical solution of nonlinear fractional integro-differential equations by hybrid functions,” Eng. Analysis Bound. Elem., 56, pp. 81–89. [CrossRef] [Google Scholar]
  23. Mashayekhi, S., and Razzaghi, M., 2016, “Numerical solution of distributed order fractional differential equations by hybrid functions,” J. Comput. Physics., 315, pp. 169–181. [CrossRef] [Google Scholar]
  24. El-Sayed A.M.A, El-Mesiry A.E.M, El-Saka HAA. Numerical solution for multi-term fractional (arbitrary) orders differential equations, Comput. appl. Math. 2004; 23: 33–54. [Google Scholar]
  25. Odibat Z, Momani S. Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos. Solitons. Fract. 2008; 36: 167–174. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.