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An approximate wavelets solution to the class of variational problems with fractional order

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Abstract

In the present work, a generalized fractional integral operational matrix is derived by using classical Legendre wavelets. Then, a numerical scheme based on this operational matrix and Lagrange multipliers is proposed for solving variational problems with fractional order. This approach has been applied on some illustrative examples. The results obtained for these examples demonstrate that the suggested technique is efficient for solving variational problems with fractional order and gives a very perfect agreement with the exact solution. The results are depicted in graphical maps and data tables. The integral square error, maximum absolute error, and order of convergence have been evaluated to analyze the precision of the suggested method. The present scheme provides better and comparable results with some other existing approaches available in the literature.

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Acknowledgements

The authors are very grateful to the reviewers for carefully reading the manuscript and for giving valuable suggestions and comments which significantly contributed to the quality and presentation of the paper.

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  1. Department of Mathematics and Statistics, Gurukula Kangri Vishwavidyalaya, Haridwar, Uttarakhand, 249404, India

    Ashish Rayal & Sag Ram Verma

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Rayal, A., Verma, S.R. An approximate wavelets solution to the class of variational problems with fractional order. J. Appl. Math. Comput. 65, 735–769 (2021). https://doi.org/10.1007/s12190-020-01413-9

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