An efficient algorithm for numerical solution of fractional integro-differential equations via Haar wavelet

• Published in: Journal of computational and applied mathematics 2021-01, Vol.381, p.113028, Article 113028
• Main Authors: Amin, Rohul, Shah, Kamal, Asif, Muhammad, Khan, Imran, Ullah, Faheem
• Format: Article
• Language: English
• Subjects: Caputo derivative; FIDEs; Haar wavelet
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2020.113028

In this paper, Haar wavelet collocation technique is developed for the solution of Volterra and Volterra–Fredholm fractional integro-differential equations. The Haar technique reduces the given equations to a system of linear algebraic equations. The derived system is then solved by Gauss elimination method. Some numerical examples are taken from literature for checking the validation and convergence of the proposed method. The maximum absolute errors are compared with the exact solution. The maximum absolute and mean square root errors for different number of collocation points are calculated. The results show that Haar method is efficient for solving these equations. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is described in the Caputo sense. All algorithms for the developed method are implemented in MATLAB (R2009b) software.