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The property of linear fractional integro-differential equations on the basis of the collocation method and the operational matrices of cubic B-spline wavelets
Abolfazl Ghasemian1*, Ali Behzadi2, Aazam Shirvani3, and Yaqub Azari4
1Department of Mathematics, Farhangian University, Yasuj, Iran.
2Department of Mathematics, Behbahan Branch, Islamic Azad University, Iran.
3Department of Computer, Farhangian University, Yasuj, Iran.
4Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16785-163
*Corresponding author’s e-mail: a.ghasemian@sru.ac.ir
Original: 21 February 2020 Revised: 21 August 2020 Accepted: 26 September 2020 Published online: 20 December 2020
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Abstract
In this paper, by using the collocation method the operational matrix of Caputo fractional derivative was constructed for the cubic B-spline scaling function and wavelets. We apply the operational matrix and the Collocation method to solve linear fractional Volterra integro-differential equations. By using the principal characteristic of this technique, we have the operational matrix, which is applied to solve any linear fractional Volterra integro-differential equation by reducing the time, computer memory occupation and convert to a system of linear equations. Finally, the validity and applicability of the new technique will be shown by some numerical examples and convergence analysis.
Key Words: Fractional integro- differential equation, Wavelet, B-spline scaling function and wavelets, Operational matrix, Error estimat, Collocation method
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