Numerical treatment of the most general linear Volterra Integro-Fractional Differential Equations with Caputo derivatives by quadrature methods

Shazad Shawki Ahmed, Shokhan Ahmed Hama Salih

Abstract


A quadrature method for numerically solving multi-order  fractional linear integro-differential equations of Volterra type with variable coefficients (VIFDE) for  and  is presented. The fractional derivative is described in the Caputo sense. The method is based on first evaluate the Caputo derivative at any fixed points by finite difference approximation and then apply quadrature method including Trapezoidal and Simpson rules to obtain a finite difference expression for our fractional equation.

Algorithm for treating linear VIFDEs using above process have been developed, in order to express these solutions, program is written in MatLab (V7.6). In addition, some numerical examples are presented to illustrate the accuracy of the method and the results of study are discussed.


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How to Cite this Article:

Shazad Shawki Ahmed, Shokhan Ahmed Hama Salih, Numerical treatment of the most general linear Volterra Integro-Fractional Differential Equations with Caputo derivatives by quadrature methods, J. Math. Comput. Sci., 2 (2012), 1293-1311

Copyright © 2012 Shazad Shawki Ahmed, Shokhan Ahmed Hama Salih. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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