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On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels

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Abstract

A wavelet-based technique has been used in this study to solve the linear and nonlinear fractional order Volterra integro-differential equations using weakly singular kernels. For solving the proposed equation, the integral operational matrix of fractional order based on the Taylor wavelets has been constructed. The fractional integral operational matrix is used to convert the linear and nonlinear fractional Volterra integro-differential equations into linear and nonlinear algebraic system of equations, respectively. Several theorems are examined for the convergence and error analysis of the proposed method. Moreover, the \(L^{2}\) and \(L^{\infty }\)-error norms have been tabulated to justify the accuracy of the presented method. Also, the results of numerical examples have been provided in both tabular and graphical form to demonstrate the efficacy and validity of the proposed methodology. Furthermore, the numerical solutions are compared to other existing methods to establish the effectiveness of the approached scheme.

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Acknowledgements

The first author sincerely acknowledges financial support from the fellowship programme “Innovation in Science Pursuit of Inspired Research (INSPIRE)” under Grant No. IF170719.

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Correspondence to Santanu Saha Ray.

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Communicated by Vasily E. Tarasov.

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Behera, S., Saha Ray, S. On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels. Comp. Appl. Math. 41, 211 (2022). https://doi.org/10.1007/s40314-022-01897-0

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  • DOI: https://doi.org/10.1007/s40314-022-01897-0

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