Author:
Ajileye Ganiyu,James Adewale
Abstract
This study presents a collocation approach for the numerical integration of multi-order fractional differential equations with initial conditions in the Caputo sense. The problem was transformed from its integral form into a system of linear algebraic equations. Using matrix inversion, the algebraic equations are solved and their solutions are substituted into the approximate equation to give the numerical results. The effectiveness and precision of the method were illustrated with the use of numerical examples.
Publisher
Nigerian Society of Physical Sciences
Subject
General Physics and Astronomy,General Mathematics,General Chemistry
Reference18 articles.
1. S.Abbas, & D.Mehdi, “A new operational matrix for solving fractional order differential equations”, Computer and Mathematics with Application 59 (2010) 1326, doi:10.1016/j.camwa.2009.07.006.
2. O. A. Uwaheren, A. F. Adebisi & O. A. Taiwo, “Perturbed Collocation Method For Solving Singular Multi-order Fractional Differential Equations of Lane-Emden Type”, Journal of the Nigerian Society of Physical Sciences 3 (2020) 141, https://doi.org/10.46481/jnsps.2020.69.
3. A. M. Wazwaz & S. M. El-Sayed, “A new modification of the Adomian decompostion method for linear and nonlinear operators”, App. Math. Comput. 122 (2001) 393.
4. R. H. Khan & H. O. Bakodah, “Adomian decomposition method and its modification for nonlinear Abel’s integral equations”, Computers and Mathematics with Applications 7 (2013) 2349.
5. R. C. Mittal & R. Nigam. ”Solution of fractional integro-differential equations by Adomiandecomposition method”, The International Journal of Applied Mathematics and Mechanics 2 (2008) 87.