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Computational method for generalized fractional Benjamin–Bona–Mahony–Burgers equations arising from the propagation of water waves

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Abstract

In this research, by utilizing the concept of the mixed Caputo fractional derivative and left-sided mixed Riemann–Liouville fractional integral, we approximate the solution of generalized fractional Benjamin–Bona–Mahony–Burgers equations (GF-BBMBEs). In addition, using Genocchi polynomial properties, we obtain a new formula to approximate the functions by Genocchi polynomials. In the process of computation, we discuss a method of obtaining the operational matrix of integration and pseudo-operational matrices of the fractional order of derivative. Also, an algorithm of obtaining the mixed fractional integral operational matrix is presented. Using the collocation method and matrices introduced, the proposed equations are converted to a system of nonlinear algebraic equations with unknown Genocchi coefficients. In addition, we discuss the upper bound of the error for the proposed method. Finally, we examine several problems to demonstrate the validity and applicability of the proposed method.

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Acknowledgements

We express our sincere thanks to the anonymous referees for valuable suggestions that improved the final manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra university, Tehran, Iran

    H Dehestani & Y Ordokhani

  2. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS, 39762, USA

    M Razzaghi

Authors
  1. H Dehestani
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  2. Y Ordokhani
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  3. M Razzaghi
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Correspondence to Y Ordokhani.

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Dehestani, H., Ordokhani, Y. & Razzaghi, M. Computational method for generalized fractional Benjamin–Bona–Mahony–Burgers equations arising from the propagation of water waves. Sādhanā 45, 95 (2020). https://doi.org/10.1007/s12046-020-1302-y

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  • DOI: https://doi.org/10.1007/s12046-020-1302-y

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