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A block-by-block method for nonlinear variable-order fractional quadratic integral equations

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Abstract

This paper is dedicated to solving a class of nonlinear fractional quadratic integral equations of variable order. The block-by-block method based on the Gauss–Lobatto quadrature technique has been developed to solve such integral equations with smooth and weakly singular kernels. In this approach, several values of the unknown functions are obtained through numerical integration without need to any starting value for beginning. The analysis of convergence of the presented method is proved and a rate of convergence is found. Some examples are solved to demonstrate the accuracy of the established approach.

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Authors and Affiliations

  1. Faculty of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    F. Afiatdoust & M. M. Hosseini

  2. Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

    M. H. Heydari

Authors
  1. F. Afiatdoust
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  2. M. H. Heydari
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  3. M. M. Hosseini
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Correspondence to M. M. Hosseini.

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Communicated by Hui Liang.

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Afiatdoust, F., Heydari, M.H. & Hosseini, M.M. A block-by-block method for nonlinear variable-order fractional quadratic integral equations. Comp. Appl. Math. 42, 38 (2023). https://doi.org/10.1007/s40314-022-02155-z

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  • DOI: https://doi.org/10.1007/s40314-022-02155-z

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