An efficient fractional-order wavelet method for fractional Volterra integro-differential equations

ABSTRACT

In this paper, an efficient and robust numerical technique is suggested to solve fractional Volterra integro-differential equations (FVIDEs). The proposed method is mainly based on the generalized fractional-order Legendre wavelets (GFLWs), their operational matrices and the Collocation method. The main advantage of the proposed method is that, by using the GFLWs basis, it can provide more efficient and accurate solution for FVIDEs in compare to integer-order wavelet basis. A comparison between the achieved results confirms accuracy and superiority of the proposed GFLWs method for solving FVIDEs. Error analysis and convergence of the GFLWs basis is provided.

Keywords:

• Fractional-order Legendre wavelets
• Caputo derivative
• operational matrix
• collocation method
• fractional Volterra integro-differential equations

2010 AMS Subject Classifications:

• 26A33
• 34A08
• 34K37
• 65T60
• 45D05

Acknowledgments

The author is grateful to the referees for their careful reading, insightful comments and helpful suggestions which have led to improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Fakhrodin Mohammadi http://orcid.org/0000-0001-9814-0367