A NUMERICAL METHOD FOR TWO-DIMENSIONAL DISTRIBUTED-ORDER FRACTIONAL NONLINEAR SOBOLEV EQUATION

Sh. Zhagharian; M. H. Heydari; M. Razzaghi

doi:10.11948/20220480

2023 Volume 13 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(5): 2630-2645

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Sh. Zhagharian, M. H. Heydari, M. Razzaghi. A NUMERICAL METHOD FOR TWO-DIMENSIONAL DISTRIBUTED-ORDER FRACTIONAL NONLINEAR SOBOLEV EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2630-2645. doi: 10.11948/20220480

Citation:

Sh. Zhagharian, M. H. Heydari, M. Razzaghi. A NUMERICAL METHOD FOR TWO-DIMENSIONAL DISTRIBUTED-ORDER FRACTIONAL NONLINEAR SOBOLEV EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2630-2645. doi: 10.11948/20220480

A NUMERICAL METHOD FOR TWO-DIMENSIONAL DISTRIBUTED-ORDER FRACTIONAL NONLINEAR SOBOLEV EQUATION

1.
Department of Mathematics, Shiraz University of Technology, Shiraz, Modarres Boulevard, 71557-13876, Iran
2.
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Author Bio: Email: s.zhagharian@sutech.ac.ir (Sh. Zhagharian); Email: razzaghi@math.msstate.edu (M. Razzaghi)
Corresponding author: Email: heydari@sutech.ac.ir (M. H. Heydari)

Abstract

Abstract

This study introduces the distributed-order fractional version of the nonlinear two-dimensional Sobolev equation. The orthonormal Chebyshev cardinal polynomials are used to construct a numerical method for this equation. To this end, some derivative matrices related to these polynomials are obtained. The proposed approach turns to solve this equation into solving a nonlinear system of algebraic equations by approximating the unknown solution using the expressed polynomials and employing their derivative matrices. The applicability and validity of this method are examined by solving three examples.
- Distributed-order fractional derivative /
- nonlinear Sobolev equation /
- Chebyshev cardinal polynomials /
- operational matrices.
MSC: 35R11, 26A33

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References

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