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Fractional analog of a chemical system inspired by Braess’ paradox

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Abstract

In this paper, we introduce the fractional analog of a chemical model arouse from a mathematical paradox attributed to Dietrich Braess. Two basic examples which serve fractional kinetic models as better suited models to the real data sets than the integer-order counterparts are given. Existence and uniqueness of the rebuilt model’s solutions are proved. It is shown that asymptotic stability conditions of the solutions are provided. A comparison is made between two different solution methods and numerical simulations are also presented to exemplify the mathematical outcomes.

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Acknowledgements

This work is supported by the Scientific Research Unit of Ankara University with the grant number 17L0430006.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ankara University, Besevler, 06100, Ankara, Turkey

    Ozlem Ozturk Mizrak & Nuri Ozalp

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  1. Ozlem Ozturk Mizrak
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  2. Nuri Ozalp
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Correspondence to Ozlem Ozturk Mizrak.

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Communicated by José Tenreiro Machado.

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Mizrak, O.O., Ozalp, N. Fractional analog of a chemical system inspired by Braess’ paradox. Comp. Appl. Math. 37, 2503–2518 (2018). https://doi.org/10.1007/s40314-017-0462-9

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  • DOI: https://doi.org/10.1007/s40314-017-0462-9

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