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A Computational Approach for the Solution of A Class of Variable-Order Fractional Integro-Differential Equations With Weakly Singular Kernels

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Abstract

A new computational approach for approximating of variable-order fractional derivatives is proposed. The technique is based on piecewise cubic spline interpolation. The method is extended to a class of nonlinear variable-order fractional integro-differential equation with weakly singular kernels. Illustrative examples are discussed, demonstrating the performance of the numerical scheme.

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Authors and Affiliations

  1. Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    Behrouz Parsa Moghaddam

  2. Department of Electrical Engineering, Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, Porto, 4249-015, Portugal

    José António Tenreiro Machado

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  1. Behrouz Parsa Moghaddam
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  2. José António Tenreiro Machado
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Correspondence to Behrouz Parsa Moghaddam.

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Moghaddam, B.P., Tenreiro Machado, J.A. A Computational Approach for the Solution of A Class of Variable-Order Fractional Integro-Differential Equations With Weakly Singular Kernels. FCAA 20, 1023–1042 (2017). https://doi.org/10.1515/fca-2017-0053

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