A computational approach for solving fractional Volterra integral equations based on two-dimensional Haar wavelet method

Abstract

In this paper, an operational matrix (OM) method based on two-dimensional Haar wavelets (2D-HWs) is proposed for solving generalized 2D fractional Volterra integral equations (2D-FVIEs). The proposed method converts these equations into an algebraic equations system. Presenting theorems, we prove the existence and uniqueness of the mentioned equations and estimate the error bound for function approximation. Our method validity and applicability are demonstrated through some examples.

Keywords:

• Two-dimensional fractional Volterra integral equations (2D-FVIEs)
• two-dimensional Haar wavelet (2D-HW)
• operational matrix (OM)

2020 Mathematics Subject Classifications:

• 65R20
• 65R30

Disclosure statement

No potential conflict of interest was reported by the author(s).