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An algorithm to estimate parameter in Müntz-Legendre polynomial approximation for the numerical solution of stochastic fractional integro-differential equation

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Abstract

In this paper, we consider the Müntz-Legendre polynomial, which is generated from the fractional basis, and develop a collocation method with the help of operational matrices to solve the stochastic fractional integro-differential equation (SFIDE). For the need of our numerical method, we introduce the operational matrices of the Müntz-Legendre polynomial for the operators involved in the SFIDE. Moreover, we proposed an algorithm with the help of the differential evolution algorithm to find the Müntz space on which we get the best results. Further, we study the convergence analysis of the proposed method. Finally, the accuracy and efficiency of the numerical method show through some test examples.

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Acknowledgements

The first author acknowledges the support provided by University Grants Commission (UGC), India, under the grant number 20/12/2015(ii)EU-V. The second author acknowledges the support provided by the SERB, a statutory body of DST, India, under the award SERB–POWER fellowship (grant number SPF/2021/000103).

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  1. Department of Mathematics, Indian Institute of Technology Delhi, 110016, New Delhi, India

    Abhishek Kumar Singh & Mani Mehra

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  1. Abhishek Kumar Singh
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  2. Mani Mehra
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Correspondence to Mani Mehra.

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Singh, A.K., Mehra, M. An algorithm to estimate parameter in Müntz-Legendre polynomial approximation for the numerical solution of stochastic fractional integro-differential equation. J. Appl. Math. Comput. 69, 2675–2694 (2023). https://doi.org/10.1007/s12190-023-01850-2

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