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Fractional-order Bessel functions with various applications

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Abstract

We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between the computed approximations and the exact solution and apply it in some examples. Applications are given to three model problems to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, P. Code: 1993893973, Iran

    Haniye Dehestani & Yadollah Ordokhani

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

    Mohsen Razzaghi

Authors
  1. Haniye Dehestani
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  2. Yadollah Ordokhani
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  3. Mohsen Razzaghi
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Correspondence to Yadollah Ordokhani.

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Dehestani, H., Ordokhani, Y. & Razzaghi, M. Fractional-order Bessel functions with various applications. Appl Math 64, 637–662 (2019). https://doi.org/10.21136/AM.2019.0279-18

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