International Scientific Journal

Authors of this Paper

External Links


In this work we suggest a numerical approach based on the B-spline polynomial to obtain the solution of linear fractional partial differential equations. We find the operational matrix for fractional integration and then we convert the main problem into a system of linear algebraic equations by using this matrix. Examples are provided to show the simplicity of our method.
PAPER REVISED: 2017-12-15
PAPER ACCEPTED: 2018-01-10
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S277 - S286]
  1. Boor, C. de, A Practical Guide to Spline, Springer-Verlag, New York, 1978.
  2. Gorenflo, R., et al., Fractional calculus and continuous-time finance. III. the Diffusion limit, in Mathematical Finance, Trends Math., (2001) pp. 171-180.
  3. Q. Huang, et al., A finite element solution for the fractional advection-dispersion equation, Advances in Water Resources, 31 (2008), 12, pp. 1578-1589.
  4. Jafari, H., An Introduction to Fractional Differential Equations, Iran, 2013.
  5. Jafari, H., et al., A decomposition method for solving the fractional Davey-Stewartson equations, International Journal of Applied and Computational Mathematics, 1 (2015), 4, pp. 559-568.
  6. Jafari, H., et al., Solutions of The Fractional Davey-Stewartson Equations with Variational Iteration Method, Romanian Reports In Physics, 64 (2012), 2, pp. 337-346.
  7. Jafari, H., Momani, S., Solving fractional diffusion and wave equations by modified homotopy perturbation method, Phys Lett A, 370 (2007) pp. 388-396.
  8. Jafari, H., et al., Homotopy analysis method for solving Abel differential equation of fractional order, Central European Journal of Physics 11 (2013), 10, pp. 1523-1527.
  9. Jafari, H., et al., Application of a homogeneous balance method to exact solutions of nonlinear fractional evolution equations, Journal of Computational and Nonlinear Dynamics, 9 (2014), 2, pp. 021019 (4 pages).
  10. Momani, S. Odibat, Z., Generalized differential transform method for solving a space and time fractional diffusion-wave equation, Physics Letters A, 370 (2007) pp. 379-387.
  11. Kilbas, A.A., et al., Theory and Application of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  12. Lakestani, M., Dehghan, M., Irandoust-pakchin, S., The construction of operational matrix of fractional derivatives using B-spline functions, Commun Nonlinear Sci Numer Simulat, 17 (2012) pp. 1149-1162.
  13. Li, X., Numerical solution of fractional differential eqiations using cubic B-spline wavelet collocation method, Commun Nonlinear Sci Numer simulat, 17 (2012) pp. 3934-3946.
  14. Lotfi, A., et al., A numerical technique for solving fractional optimal control problems, Comput. Math. Appl,. 62 (2011) pp. 1055-1067.
  15. Tian, W., Polynomial spectral collocation method for space fractional advection-diffusion equation, Numerical Methods for Partial Differential Equations, 30 (2014) 514-535.
  16. Podlubny, I., Fractional Differential Equations, Academic Press, New York, 1999.
  17. Samko, S. et al., Fractional Integrals and derivatives: Theory and Applications. Gordon and Breach Science Publishers, Yverdon, 1993.
  18. Rostamy, D., et al., Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis, Romanian Reports in Physics, 65 (2013), 2, pp. 334-349.
  19. Saadatmandi , A. Dehghan, M., A new operational matrix for solving fractional-order differential equations, Computers and Mathematics with Applications, 59 (2010) pp. 1326-1336.
  20. Wang, L. et al., Haar wavelet method for solving fractional partial differential equations numerically, Applied Mathematics and Computation, 227 (2014) pp. 66-76.
  21. Wu, J.L., A wavelet operational method for solving fractional partial differential equations numerically, Applied Mathematics and Computation 214 (2009) pp. 31-40.

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence