What question did this study set out to answer?

To develop an improved high-order numerical scheme for solving 2D general fractional nonlinear Volterra integral equations.

An improved high-order uniform accuracy scheme for nonlinear system of 2D general fractional Volterra integral equations

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Randomized trial demonstrates improved numerical solving of 2D fractional Volterra equations, suggesting enhanced accuracy.

To develop an improved high-order numerical scheme for solving 2D general fractional nonlinear Volterra integral equations.
Applied fixed point theory for existence and uniqueness of solutions.
Developed a numerical scheme via modified block-by-block method and biquadratic interpolation.
Utilized dimensionality reduction techniques and discrete Grönwall inequality for convergence analysis.
Achieved a convergence order of O(h1^(3+θ1) + h2^(3+θ2)) with θ1, θ2 between 0 and 1.
Validated method efficacy through numerical experiments, effectively addressing both smooth and non-smooth solutions.

Wang et al. (2026) studied this question.

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