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

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.

Automated summary

The paper introduces an operational matrix method based on two-dimensional Haar wavelets for solving generalized 2D fractional Volterra integral equations. By presenting theorems, the existence and uniqueness of the equations are proven, and the error bound for function approximation is estimated. The validity and applicability of the method are demonstrated through examples.