An Efficient Numerical Approach for Approximating Nonlocal Variable-Order Weakly Singular Integro-Differential Equations
Subject Areas : Numerical Analysis
Nayereh Tanha
1
,
Behrouz Parsa Moghaddam
2
,
Mousa Ilie
3
1 - Islamic Azad University, Lahijan Branch
2 - Islamic Azad University, Lahijan Branch
3 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
Keywords: Fractional calculus \sep Variable-order fractional derivative \sep Fractional differential equations, Spline interpolation, Numerical optimization, Weakly singular integro-differential equations.,
Abstract :
This paper presents an efficient numerical method for approximating variable-order fractional derivatives using an Integro spline quasi-interpolation approach. The proposed technique is extended to address nonlocal variable-order weakly singular integro-differential equations. Several illustrative examples are provided to validate the effectiveness and performance of the numerical scheme. Additionally, the optimal error orders are determined by minimizing the mean absolute error, demonstrating the method’s accuracy and computational efficiency.
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