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Structure preserving computational technique for fractional order Schnakenberg model

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Abstract

The current article deals with the analysis and numerical solution of fractional order Schnakenberg (S-B) model. This model is a system of autocatalytic reactions by nature, which arises in many biological systems. This study is aiming at investigating the behavior of natural phenomena with a more realistic and practical approach. The solutions are obtained by applying the Grunwald–Letnikov (G–L) finite difference (FD) and the proposed G–L nonstandard finite difference (NSFD) computational schemes. The proposed formulation is explicit in nature, strongly structure preserving as well as it is independent of the time step size. One very important feature of our proposed scheme is that it preserves the positivity of the solution of continuous fractional order S-B model because the unknown variables involved in this system describe the chemical concentrations of different substances. The comparison of the proposed scheme with G–L FD method reflects the significance of the said method.

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Acknowledgements

We would like to express our sincere thanks to reviewers for the careful reading and helpful remarks of our paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Zafar Iqbal, Nauman Ahmed & Muhammad Aziz-ur Rehman

  2. Department of Mathematics, Cankaya University, Balgat, 06530, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

  4. Faculty of Engineering, University of Central Punjab, Lahore, Pakistan

    Muhammad Rafiq

  5. Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan

    Zafar Iqbal, Nauman Ahmed & Muhammad Sajid Iqbal

Authors
  1. Zafar Iqbal
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  2. Nauman Ahmed
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  3. Dumitru Baleanu
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  4. Muhammad Rafiq
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  5. Muhammad Sajid Iqbal
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  6. Muhammad Aziz-ur Rehman
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Corresponding author

Correspondence to Nauman Ahmed.

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Communicated by José Tenreiro Machado.

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Iqbal, Z., Ahmed, N., Baleanu, D. et al. Structure preserving computational technique for fractional order Schnakenberg model. Comp. Appl. Math. 39, 61 (2020). https://doi.org/10.1007/s40314-020-1068-1

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  • DOI: https://doi.org/10.1007/s40314-020-1068-1

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