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Numerical Treatment Solution of Volterra Integro-Fractional Differential Equation by Using Linear Spline Function


Karwan H.F. Jwamer 1, Shazad Sh. Ahmed 1 and  Diar Kh. Abdullah1*


1Department of Mathematics, College of Science, Sulaimani University, Sulaimani, Kurdistan Region, Iraq.

*Corresponding author:[email protected]

Original: 5 August 2020        Revised: 1 September 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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In this article, we propose two new approximate methods based totally on the use of normal linear spline function and second employed with the Richardson Extrapolation technique the usage of discrete collocation points for approximating the solution of the Volterra integro-fractional differential equations (VIFDEs). The fractional derivatives are used in the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the technique. A new technique with the resource of MatLab program is written to treat numerically VIFDEs using spline function, as well as, follow the Clenshaw Curtis rule for calculating the required integrals for those equations.

Key Words: Integro- fractional differential equation, Caputo derivative, Linear spline, Extrapolation method, Clenshaw