Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel

Sania Qureshi and Shaheen Aziz

Physica A: Statistical Mechanics and its Applications, 2020, vol. 542, issue C

Abstract: Various physical systems exhibit non-Markovian (hereditary and memory effects) characteristics in their very inherent structures. In this research study, the fractional (non-classical) differential operator of Caputo’s type is used to analyze such a physical system representing chemical kinetic reactions in a batch reactor. The governing system of fractional order equations under Caputo’s type derivative is formulated and later solved via Laplace integral transform and its inversion. Analytically obtained general solutions of the governing equations are expressed in the form of special Mittag-Leffler function and power series expansion with double summation. During fractionalization, the dimensional analysis has been taken care of and the results are graphically illustrated. The obtained simulation results for varying values of fractional-order α represented various behavior with the fractional Caputo’s type governing equations for the concentration of three species. In other words, varying memory effects are observed during simulations of the model based upon different values of α and the rate constants. The classical model is retrieved for the limiting case when α→1.

Keywords: Caputo; Mittag-Leffler; Power law; Laplace; Concentration; Power series (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119319508

DOI: 10.1016/j.physa.2019.123494

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