An Efficient Numerical Approach for Approximating Nonlocal Variable-Order Weakly Singular Integro-Differential Equations
محورهای موضوعی : Numerical Analysis
Nayereh Tanha
1
,
Behrouz Parsa Moghaddam
2
,
Mousa Ilie
3
1 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
3 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
کلید واژه: Fractional calculus \sep Variable-order fractional derivative \sep Fractional differential equations, Spline interpolation, Numerical optimization, Weakly singular integro-differential equations.,
چکیده مقاله :
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.
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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